75 lines
1.6 KiB
Plaintext
75 lines
1.6 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Euler Problem 29\n",
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"\n",
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"Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:\n",
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"\n",
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"$2^2=4, 2^3=8, 2^4=16, 2^5=32$\n",
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"\n",
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"$3^2=9, 3^3=27, 3^4=81, 3^5=243$\n",
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"\n",
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"$4^2=16, 4^3=64, 4^4=256, 4^5=1024$\n",
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"\n",
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"$5^2=25, 5^3=125, 5^4=625, 5^5=3125$\n",
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"\n",
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"If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:\n",
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"\n",
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"$4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125$\n",
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"\n",
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"How many distinct terms are in the sequence generated by $a^b$ for $2 ≤ a ≤ 100$ and $2 ≤ b ≤ 100$?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"9183\n"
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]
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}
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],
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"source": [
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"s = len(set([a**b for a in range(2, 101) for b in range(2, 101)]))\n",
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"assert(s == 9183)\n",
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"print(s)"
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]
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}
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],
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"metadata": {
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"completion_date": "Fri, 25 Aug 2017, 10:03",
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.4"
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},
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"tags": [
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"distinct",
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"powers"
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]
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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