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number n \choose i + n \choose j -i -j is even

Source: 2013 Grand Duchy of Lithuania, Mathematical Contest p4 (Baltic Way TST)

October 3, 2020
Combinationsnumber theoryEven

Problem Statement

A positive integer n≥2n \ge 2 is called peculiar if the number (ni)n \choose i + (nj)n \choose j −i−j-i-j is even for all integers ii and jj such that 0≤i≤j≤n0 \le i \le j \le n. Determine all peculiar numbers.
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