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Never a square (Posted on 2017-02-26) Difficulty: 4 of 5
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.

No Solution Yet Submitted by Ady TZIDON    
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Hints/Tips re(3): Poossible solution...very creative! | Comment 4 of 5 |
(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!

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
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