Let each of x₁, x₂, x₃, …, x₇₇₇, y₁, y₂, y₃, …, y₇₇₇ be an arbitrary non-zero integer number.
Consider the product

P = (2x₁² +3y₁²) * (2x₂² +3y₂²) * (2x₃² +3y₃²) * ...* (2x₇₇₇² +3y₇₇₇²).

Prove: P cannot be a square number.

(In reply to re: Poossible solution...very creative! by Ady TZIDON)

x^2 + 6y^2 plainly contains all the squares, when y = 0.

Since the two sequences contain no common members, hence 'chalk' and 'cheese', the result follows at once.

Posted by broll on 2017-02-27 05:02:09