# A non-constant polynomial which always takes non-square integers

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• October 28th 2009, 12:11 PM
gabor7896
A non-constant polynomial which always takes non-square integers
Hi!
I can't solve this problam:

Does there exist a non-constant polynomial which always takes non-square integers at integer values of the variables?

How can I prove the solution?
• October 28th 2009, 12:37 PM
Bruno J.
Yes, for example $f(n)=4n+3$, because squares are always congruent to 1 or to 0 modulo 4.