Let each of

**x**_{1}, x_{2}, x_{3}, …, x_{777}, y_{1}, y_{2}, y_{3}, …, y_{777} be an arbitrary non-zero integer number.

Consider the product

P = (2x_{1}^{2} +3y_{1}^{2}) *
(2x_{2}^{2} +3y_{2}^{2}) * (2x_{3}^{2} +3y_{3}^{2}) * ...* (2x_{777}^{2} +3y_{777}^{2}).

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.