perplexus.info :: Just Math : Near Fermat Formulation

Near Fermat Formulation (Posted on 2015-05-11)

Prove that the equation:
A^N + B^N = C^N-1
has an infinity of positive integer solutions for every integer value of N ≥ 2

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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solution

| Comment 1 of 4

let A=B=2^(n-2) and C=2^(n-1)

then we have

A^n+B^n=

[2^(n-2)]^n+[2^(n-2)]^n

2*[2^(n-2)]^n

2*2^(n*(n-2))

2*2^(n^2-2n)

2^(n^2-2n+1)

2^((n-1)^2)

[2^(n-1)]^(n-1)=C^(n-1)

Posted by Daniel on 2015-05-11 13:20:55

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