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.
(In reply to Poossible solution
Very interesting and very original approach!
However: you say "the sequence 'Cheese' contains none"...
How do we know that? (i.e. please substantiate!).
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.