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.
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