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Congruence relation with binomial coefficients

Source: Netherlands IMO Team Selection Test 2013

October 21, 2014

modular arithmeticnumber theory unsolvednumber theory

Problem Statement

Determine all positive integers

n\ge 2

satisfying

i+j\equiv\binom ni +\binom nj \pmod{2}

for all

i

and

j

with

0\le i\le j\le n