MathDB

parity of C(n,k)

Source: Iran TST 2012 -first day- problem 1

April 23, 2012

modular arithmeticpolynomialnumber theorylucas theorem

Problem Statement

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