IMO 1996 SL N5

Let … denote the set of nonnegative integers. Find a bijective function … from … into … such that for all …,

imoshortlistmathematicsolympiadnumber theory

IMO 1996 SL N5

Origin: ROM | Category: Number Theory

Problem

Let $N_0$ denote the set of nonnegative integers. Find a bijective function $f$ from $N_0$ into $N_0$ such that for all $m, n \in N_0$,

$$f(3mn + m + n) = 4f(m)f(n) + f(m) + f(n).$$