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i+j = C_{n}^{i} + C_{n}^{j} (mod 2)

Source: Ukraine TST 2014 p5

April 30, 2020

Integersnumber theorymodulo

Problem Statement

Find all positive integers

n \ge 2

such that equality

i+j \equiv C_{n}^{i} + C_{n}^{j}

(mod

2

) is true for arbitrary

0 \le i \le j \le n