MathDB

Let an ordered pair of positive integers

(m, n)

be called regimented if for all nonnegative integers

k

, the numbers

m^k

and

n^k

have the same number of positive integer divisors. Let

N

be the smallest positive integer such that

\left(2016^{2016}, N\right)

is regimented. Compute the largest positive integer

v

such that

2^v

divides the difference

2016^{2016}-N

.
Proposed by Ashwin Sah

Problem Statement