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Math Help - A non-constant polynomial which always takes non-square integers

  1. #1
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    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?
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Yes, for example f(n)=4n+3, because squares are always congruent to 1 or to 0 modulo 4.
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