Problem

Source: Iran TST 2012 -first day- problem 1

Tags: modular arithmetic, polynomial, number theory, lucas theorem



Find all positive integers $n \geq 2$ such that for all integers $i,j$ that $ 0 \leq i,j\leq n$ , $i+j$ and $ {n\choose i}+ {n \choose j}$ have same parity. Proposed by Mr.Etesami