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Distinct Powers (Posted on 2024-02-20) |
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How many distinct terms are in the sequence generated by a^b for integers a and b, where 2 ≤ a ≤ 100, and 2 ≤ b ≤ 100? Can you find the answer without computing the value of each a^b? (Project Euler problem #29)
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Submitted by Steven Lord
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Solution:
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Answer: 9183 are distinct. I solved this by using the prime factorizations of "a" from 2 to 100. I then raised these to the powers b = 2 to 100 by multiplying the individual prime factor exponents by b. Lastly, I counted duplicate sets of prime factor exponents. |
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