A number theory problem by Akeel Howell

Number Theory Level 1

Is 2 n 2^{n} ever a multiple of 6 6 for positive integers n n ?

Cannot be determined Yes No

Akeel Howell by Akeel Howell , 22, USA

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1 solution

Anthony Holm
Sep 22, 2016

Any multiple of 6 must also be a multiple of 3 and 2. Obviously all powers of 2 are multiples of 2, but no power of 2 is a multiple of 3 as the prime factorization of 2^n is simply 2^n, and there are no factors of 3.

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