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Math Help - Find the maximum value...

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    Find the maximum value...

    Find the maximum value of the positive integer n for which (n^2) + 2 divides f(n) = (n+1)((n^4)+2n) + 3((n^3)+57)
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    Quote Originally Posted by MATNTRNG View Post
    Find the maximum value of the positive integer n for which (n^2) + 2 divides f(n) = (n+1)((n^4)+2n) + 3((n^3)+57)
    If n^2+2 divides (n+1)(n^4+2n) + 3(n^3+57) = n^5+n^4+3n^3+2n^2+2n+171 = (n^2+2)(n^3+n^2+n) + 171, then n^2+2 must divide 171. The largest integer n with that property is n = 13.
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