MathDB

M={x^2+x}

Source: Moldavian Republic Olympiad

March 5, 2006

modular arithmeticinductionnumber theory unsolvednumber theory

Problem Statement

Let

M=\{x^2+x \mid x\in \mathbb N^{\star} \}

. Prove that for every integer

k\geq 2

there exist elements

a_{1}, a_{2}, \ldots, a_{k},b_{k}

from

M

, such that

a_{1}+a_{2}+\cdots+a_{k}=b_{k}