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 re: solution by broll)

Are a quarter of the numbers be divisible by 4?  If so, why should it be every other number divisible by 2?  Are one-seventh of the numbers M^M+1 divisible by 7?  Is it every seventh number?

The answers to these may be 'yes' but I think the proof is needed.  So I did the math to prove it.

Posted by Jer on 2014-05-02 12:39:33