MathDB

1

Part of 1901 Eotvos Mathematical Competition

Problems(1)

Prove that, for any positive integer $n$, $$1^n+2^n+3^n+4^n$$ is divisible by $5

Source: Eotvos 1901 p1

3/19/2020
Prove that, for any positive integer nn, 1n+2n+3n+4n1^n+2^n+3^n+4^n is divisible by 55 if and only if nn is not divisible by 44.
algebra