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Getting Primed With Squares (Posted on 2008-07-27) Difficulty: 2 of 5
Determine all possible pair(s) of primes (M, N) such that each of M+N and M-N is a perfect square.

See The Solution Submitted by K Sengupta    
Rating: 2.0000 (1 votes)

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Solution | Comment 1 of 2

M+N=AČ, M-N=BČ

2N=AČ-BČ=(A-B)(A+B)

A-B cant equal 1, since then A+B=2N, but A-B and A+B must have the same parity. Thus A-B=2, A+B=N, -> N=2B+2, which shows that N is divisible by 2. Since N is prime, N must equal 2, which gives B=0 and then M=2.

Answer: the only pair is (2,2)


  Posted by Jonathan Lindgren on 2008-07-27 17:06:59
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