Let each of
x_{1}, x_{2}, x_{3}, …, x_{777}, y_{1}, y_{2}, y_{3}, …, y_{777} be an arbitrary nonzero 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.
Let the sequence x^2 + 6y^2 {1, 4, 6, 7, 9, 10, 15, 16,..} be 'Chalk'; let the sequence 2x^2 + 3y^2 {0, 2, 3, 5, 8, 11, 12, 14, 18, 20...)be 'Cheese'.
Cheese*Cheese = Chalk; e.g. = 2*2 = 4, 5*2=10.
Cheese*Chalk = Cheese; e.g.2*4=8,4*3=12,2*10=20.
The sequence 'Chalk' contains every square; the sequence 'Cheese' contains none.
Hence P cannot be square.

Posted by broll
on 20170227 01:21:33 