Let us consider the expression M^M+1, where M is a positive integer.

It can be verified that M=3 is the least value for which 2² divides M^M+1.

Given that n is a positive integer, find the least value of M (in terms of n) for which M^M+1 is divisible by 2ⁿ.

(In reply to some examples by Charlie)

We want M^M+1 not M^M to be divisible by 2ⁿ.

n  2n   M    MM+1
1   2   1       2
2   4   3      28  
3   8   7  823544
4  16  15  (large)

Posted by Jer on 2014-05-01 16:47:40