MathDB

Let

\mathbb{Z}^+

denote the set of all positive integers. Find all surjective functions

f:\mathbb{Z}^+ \times \mathbb{Z}^+ \rightarrow \mathbb{Z}^+

that satisfy all of the following conditions: for all

a,b,c \in \mathbb{Z}^+

, (i)

f(a,b) \leq a+b

; (ii)

f(a,f(b,c))=f(f(a,b),c)

(iii)Both

\binom{f(a,b)}{a}

and

\binom{f(a,b)}{b}

are odd numbers.(where

\binom{n}{k}

denotes the binomial coefficients)

Problem Statement