MathDB
f(3mn + m + n) = 4f(m)f(n) + f(m) + f(n)

Source: IMO Shortlist 1996, N5

August 9, 2008
functionnumber theoryFunctional EquationsIMO Shortlist

Problem Statement

Show that there exists a bijective function f:N0→N0 f: \mathbb{N}_{0}\to \mathbb{N}_{0} such that for all m,n∈N0 m,n\in \mathbb{N}_{0}: f(3mn \plus{} m \plus{} n) \equal{} 4f(m)f(n) \plus{} f(m) \plus{} f(n).
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