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(2): Poossible solution...very creative! by broll)

y cannot be 0 , the text implies non-zero integers.

Still, properly modified, you might converge to formal proof.

Please, while editing erase the 1st 0 in the brackets- correcting the pOOsible  word is impossible!

btw:
My solution (took me a long time to reach it) is much simpler - just notice that 2x^2 is never 1 mod 3.

Posted by Ady TZIDON on 2017-02-27 07:05:58