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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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Some Thoughts re(2): Poossible solution...very creative! | Comment 3 of 5 |
(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
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