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(x^2+p t^2)(y^2+p t^2)(z^2+p t^2) is a perfect square when (x, y, z, t) distinct

Source: SRMC 2009

September 2, 2018
number theoryPerfect Squareprime

Problem Statement

Prove that for any prime number pp there are infinitely many fours (x,y,z,t)(x, y, z, t) pairwise distinct natural numbers such that the number (x2+pt2)(y2+pt2)(z2+pt2)(x^2+p t^2)(y^2+p t^2)(z^2+p t^2) is a perfect square.
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