5

Part of 2014 Ukraine Team Selection Test

Problems(1)

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

Source: Ukraine TST 2014 p5

Find all positive integers

n \ge 2

such that equality

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

2

) is true for arbitrary

0 \le i \le j \le n

Integersnumber theorymodulo