perplexus.info :: Just Math : Powerful Divisor

Powerful Divisor (Posted on 2014-05-01)

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.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The largest power of 2 that divides M+1 is the largest power of 2 that divides M^M+1.
For an explanation, refer to the solution submitted by Jer in this location.
.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re(2): solution	Jer	2014-05-02 12:39:33
re: solution	broll	2014-05-02 09:38:04
re: some examples	Jer	2014-05-01 16:47:40
uh oh	Charlie	2014-05-01 16:42:57
solution	Jer	2014-05-01 16:38:40
re: more examples	Charlie	2014-05-01 16:37:49
more examples	Charlie	2014-05-01 16:35:40
some examples	Charlie	2014-05-01 16:28:34

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