perplexus.info :: Just Math : Nimble Exponent Extrication

Nimble Exponent Extrication (Posted on 2021-11-22)

How many integer values of n satisfy this equation?

(6+n)ⁿ + (7+n)ⁿ = 12ⁿ + 1

Prove that there are no others.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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First thoughts

| Comment 1 of 3

Obviously, 0 works.

Also, obviously, n must be less than 5. If n is 5 or greater, the left hand side is larger than the right hand side.

And no negative numbers work.

So the only possible values or 0,1,2,3, and 4.

I am too lazy to actually try them, but it is simple enough to do.

Posted by Steve Herman on 2021-11-22 08:42:59

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