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Square OR 2*square (Posted on 2017-01-14) Difficulty: 4 of 5
Given p is a prime number and that there are 2 distinct positive integers u and v such that p^2 is the mean of u^2 and v^2.

Prove that 2p−u−v is either a square or twice a square.

No Solution Yet Submitted by Ady TZIDON    
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reference Comment 2 of 2 |
2p^2 = u^2 + v^2

Substituting u = (a-b) and v = (a+b) gives p^2 = a^2 + b^2 so (a,b,p) is a pythagorean triplet.  Using the parametric assignments to build up to u and v gives broll's solution.

This link was a great help:  http://math.stackexchange.com/questions/1282600/parametric-characterization-for-x2-y2-2z2

  Posted by xdog on 2017-01-15 14:55:02
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