Figured out problem with Fermat test in problem 58.
This commit is contained in:
@@ -11846,7 +11846,7 @@ div#notebook {
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<span class="k">return</span> <span class="p">(</span><span class="n">base</span> <span class="o">*</span> <span class="n">expmod</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="n">exp</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">m</span><span class="p">)</span> <span class="o">%</span> <span class="n">m</span><span class="p">)</span>
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<span class="k">def</span> <span class="nf">fermat_test</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
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<span class="k">def</span> <span class="nf">fermat_test_sicp</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
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<span class="k">if</span> <span class="n">n</span> <span class="o"><</span> <span class="mi">40</span><span class="p">:</span>
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<span class="k">return</span> <span class="n">n</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">13</span><span class="p">,</span> <span class="mi">17</span><span class="p">,</span> <span class="mi">19</span><span class="p">,</span> <span class="mi">23</span><span class="p">,</span> <span class="mi">29</span><span class="p">,</span> <span class="mi">31</span><span class="p">,</span> <span class="mi">37</span><span class="p">,</span> <span class="mi">39</span><span class="p">]</span>
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<span class="n">a</span> <span class="o">=</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">3</span>
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@@ -11910,10 +11910,10 @@ div#notebook {
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<span class="k">return</span> <span class="kc">False</span>
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<span class="k">return</span> <span class="n">trial_division</span><span class="p">(</span><span class="n">n</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="n">n</span>
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<span class="k">assert</span><span class="p">(</span><span class="n">fermat_test</span><span class="p">(</span><span class="mi">3</span><span class="p">))</span>
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<span class="k">assert</span><span class="p">(</span><span class="n">fermat_test</span><span class="p">(</span><span class="mi">107</span><span class="p">))</span>
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<span class="k">assert</span><span class="p">(</span><span class="n">fermat_test</span><span class="p">(</span><span class="mi">108</span><span class="p">)</span> <span class="o">==</span> <span class="kc">False</span><span class="p">)</span>
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<span class="k">assert</span><span class="p">(</span><span class="n">fermat_test</span><span class="p">(</span><span class="mi">109</span><span class="p">))</span>
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<span class="k">assert</span><span class="p">(</span><span class="n">fermat_test_sicp</span><span class="p">(</span><span class="mi">3</span><span class="p">))</span>
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<span class="k">assert</span><span class="p">(</span><span class="n">fermat_test_sicp</span><span class="p">(</span><span class="mi">107</span><span class="p">))</span>
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<span class="k">assert</span><span class="p">(</span><span class="n">fermat_test_sicp</span><span class="p">(</span><span class="mi">108</span><span class="p">)</span> <span class="o">==</span> <span class="kc">False</span><span class="p">)</span>
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<span class="k">assert</span><span class="p">(</span><span class="n">fermat_test_sicp</span><span class="p">(</span><span class="mi">109</span><span class="p">))</span>
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</pre></div>
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</div>
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</div>
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@@ -11989,7 +11989,7 @@ div#notebook {
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</div>
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<div class="cell border-box-sizing code_cell rendered">
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<div class="input">
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<div class="prompt input_prompt">In [5]:</div>
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<div class="prompt input_prompt">In [12]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">random</span>
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@@ -11997,27 +11997,14 @@ div#notebook {
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<span class="k">def</span> <span class="nf">is_prime</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
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<span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
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<span class="k">return</span> <span class="kc">False</span>
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<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">):</span>
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<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">):</span>
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<span class="n">a</span> <span class="o">=</span> <span class="n">n</span> <span class="o">-</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
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<span class="k">if</span> <span class="ow">not</span> <span class="n">expmod</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span> <span class="o">==</span> <span class="n">a</span><span class="p">:</span>
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<span class="k">return</span> <span class="kc">False</span>
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<span class="k">return</span> <span class="kc">True</span>
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<span class="k">assert</span><span class="p">(</span><span class="n">fermat_test</span><span class="p">(</span><span class="mi">3</span><span class="p">))</span>
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<span class="k">assert</span><span class="p">(</span><span class="n">fermat_test</span><span class="p">(</span><span class="mi">107</span><span class="p">))</span>
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<span class="k">assert</span><span class="p">(</span><span class="n">fermat_test</span><span class="p">(</span><span class="mi">108</span><span class="p">)</span> <span class="o">==</span> <span class="kc">False</span><span class="p">)</span>
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<span class="k">assert</span><span class="p">(</span><span class="n">fermat_test</span><span class="p">(</span><span class="mi">109</span><span class="p">))</span>
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</pre></div>
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</div>
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</div>
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</div>
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</div>
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<div class="cell border-box-sizing code_cell rendered">
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<div class="input">
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<div class="prompt input_prompt">In [6]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">s</span> <span class="o">=</span> <span class="n">get_solution</span><span class="p">()</span>
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<span class="nb">print</span><span class="p">(</span><span class="n">get_solution</span><span class="p">())</span>
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<span class="nb">print</span><span class="p">(</span><span class="s2">"Expected n is 26241."</span><span class="p">)</span>
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</pre></div>
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</div>
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</div>
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@@ -12028,6 +12015,8 @@ div#notebook {
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<div class="prompt"></div>
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<div class="output_subarea output_stream output_stdout output_text">
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<pre>n: 26641 count_total: 53281 count_primes: 5328 ratio: 0.09999812315834913
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26641
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Expected n is 26241.
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</pre>
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</div>
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</div>
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@@ -12046,6 +12035,70 @@ div#notebook {
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</div>
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<div class="cell border-box-sizing code_cell rendered">
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<div class="input">
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<div class="prompt input_prompt">In [10]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">carmichael_number</span> <span class="o">=</span> <span class="p">[</span><span class="mi">561</span><span class="p">,</span> <span class="mi">1105</span><span class="p">,</span> <span class="mi">1729</span><span class="p">,</span> <span class="mi">2465</span><span class="p">,</span> <span class="mi">2821</span><span class="p">,</span> <span class="mi">6601</span><span class="p">]</span>
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<span class="k">def</span> <span class="nf">little_fermat</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">p</span><span class="p">):</span> <span class="c1"># SICP uses this</span>
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<span class="k">return</span> <span class="p">(</span><span class="n">a</span> <span class="o">**</span> <span class="n">p</span><span class="p">)</span> <span class="o">%</span> <span class="n">p</span> <span class="o">==</span> <span class="n">a</span> <span class="o">%</span> <span class="n">p</span>
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<span class="k">def</span> <span class="nf">little_fermat_simple</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">p</span><span class="p">):</span> <span class="c1"># Wikipedia uses this</span>
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<span class="k">assert</span><span class="p">(</span><span class="n">a</span> <span class="o"><</span> <span class="n">p</span><span class="p">)</span>
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<span class="k">return</span> <span class="p">(</span><span class="n">a</span> <span class="o">**</span> <span class="p">(</span><span class="n">p</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))</span> <span class="o">%</span> <span class="n">p</span> <span class="o">==</span> <span class="mi">1</span>
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<span class="k">def</span> <span class="nf">expmod</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="n">exp</span><span class="p">,</span> <span class="n">m</span><span class="p">):</span>
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<span class="k">if</span> <span class="n">exp</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
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<span class="k">return</span> <span class="mi">1</span>
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<span class="k">if</span> <span class="p">(</span><span class="n">exp</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">):</span>
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<span class="k">return</span> <span class="p">(</span><span class="n">expmod</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="n">exp</span> <span class="o">//</span> <span class="mi">2</span><span class="p">,</span> <span class="n">m</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">%</span> <span class="n">m</span><span class="p">)</span>
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<span class="k">return</span> <span class="p">(</span><span class="n">base</span> <span class="o">*</span> <span class="n">expmod</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="n">exp</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">m</span><span class="p">)</span> <span class="o">%</span> <span class="n">m</span><span class="p">)</span>
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<span class="k">def</span> <span class="nf">fermat_test</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
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<span class="n">ps</span> <span class="o">=</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">13</span><span class="p">,</span> <span class="mi">17</span><span class="p">,</span> <span class="mi">19</span><span class="p">,</span> <span class="mi">23</span><span class="p">,</span> <span class="mi">29</span><span class="p">,</span> <span class="mi">31</span><span class="p">,</span> <span class="mi">37</span><span class="p">,</span> <span class="mi">39</span><span class="p">]</span>
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<span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="n">ps</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
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<span class="k">return</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">ps</span>
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<span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">ps</span><span class="p">:</span>
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<span class="c1">#if not little_fermat_simple(a, n):</span>
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<span class="k">if</span> <span class="n">expmod</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">:</span>
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<span class="c1">#print("Fermat witness for {} is {}.".format(n + 1, a))</span>
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<span class="k">return</span> <span class="kc">False</span>
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<span class="k">return</span> <span class="kc">True</span>
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<span class="k">def</span> <span class="nf">is_prime</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
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<span class="k">return</span> <span class="n">fermat_test</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
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<span class="nb">print</span><span class="p">(</span><span class="n">get_solution</span><span class="p">())</span>
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<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">carmichael_number</span><span class="p">:</span>
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<span class="n">r_sicp</span> <span class="o">=</span> <span class="n">fermat_test_sicp</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
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<span class="n">r</span> <span class="o">=</span> <span class="n">fermat_test</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
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<span class="nb">print</span><span class="p">(</span><span class="s2">"For </span><span class="si">{}</span><span class="s2"> sicp says </span><span class="si">{}</span><span class="s2"> and real test says </span><span class="si">{}</span><span class="s2">."</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">r_sicp</span><span class="p">,</span> <span class="n">r</span><span class="p">))</span>
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</pre></div>
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</div>
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</div>
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</div>
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<div class="output_wrapper">
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<div class="output">
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<div class="output_area">
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<div class="prompt"></div>
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<div class="output_subarea output_stream output_stdout output_text">
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<pre>n: 26241 count_total: 52481 count_primes: 5248 ratio: 0.09999809454850327
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26241
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For 561 sicp says True and real test says False.
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For 1105 sicp says True and real test says False.
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For 1729 sicp says True and real test says False.
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For 2465 sicp says True and real test says False.
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For 2821 sicp says True and real test says False.
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For 6601 sicp says True and real test says False.
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</pre>
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</div>
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</div>
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</div>
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</div>
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</div>
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<div class="cell border-box-sizing code_cell rendered">
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<div class="input">
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<div class="prompt input_prompt">In [ ]:</div>
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<div class="inner_cell">
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<div class="input_area">
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Reference in New Issue
Block a user