1998 AHSME Problem 12

Number Theory Level 2

How many different prime numbers are factors of N if log ⁡ 2 ( log ⁡ 3 ( log ⁡ 5 ( log ⁡ 7 N ) ) ) \log_2 (\log_3 (\log_5 (\log_7 N))) = 11?

2 1 7 3

Daniel Hirschberg by Daniel Hirschberg , 39, USA

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1 solution

Alex Segesta
May 10, 2014

7 5 3 2 11 7^{5^{3^{2^{11}}}} has only 1 prime factor: 7

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