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 Never a square (Posted on 2017-02-26)
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 No Rating

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 re: Poossible solution...very creative! | Comment 2 of 5 |
(In reply to Poossible solution by broll)

Very interesting and very original approach!

However: you say "the sequence 'Cheese' contains none"...

How do we know that?  (i.e. please substantiate!).

Another approach:
consider a typical expression within brackets modulo 3 and then modulo 2,-  show that it is impossible for both the powers of 2 and of 3 within the final product be even while  the number of terms is odd.

 Posted by Ady TZIDON on 2017-02-27 04:41:25

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