olymmath

TH-TMO 2005 Problem 14

    A function f:Z→Zf : Z \to Z is given so that f(m+n)=f(m)+f(n)+2mn−2548f(m + n) = f(m) + f(n) + 2mn - 2548 for all positive integers m,nm, n . Given that f(2548)=−2548f(2548) = -2548 , find the value of f(2)f(2) .

    Dataset text AI-MO AoPS. Quoted with source.

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