# Euler Problem 29¶

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Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

$2^2=4, 2^3=8, 2^4=16, 2^5=32$

$3^2=9, 3^3=27, 3^4=81, 3^5=243$

$4^2=16, 4^3=64, 4^4=256, 4^5=1024$

$5^2=25, 5^3=125, 5^4=625, 5^5=3125$

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

$4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125$

How many distinct terms are in the sequence generated by $a^b$ for $2 ≤ a ≤ 100$ and $2 ≤ b ≤ 100$?

In [1]:

    s = len(set([a**b for a in range(2, 101) for b in range(2, 101)]))
    assert(s == 9183)
    print(s)

    9183