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f(m + f(f(n))) = -f(f(m+ 1) - n

Source: IMO ShortList 1991, Problem 23 (IND 2)

August 15, 2008
functionalgebrapolynomialfunctional equationIMO Shortlist

Problem Statement

Let f f and g g be two integer-valued functions defined on the set of all integers such that (a) f(m \plus{} f(f(n))) \equal{} \minus{}f(f(m\plus{} 1) \minus{} n for all integers m m and n; n; (b) g g is a polynomial function with integer coefficients and g(n) = g(f(n)) g(f(n)) ∀n∈Z. \forall n \in \mathbb{Z}.
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