MathDB

Given any integer

n \geq 2,

assume that the integers

a_1, a_2, \ldots, a_n

are not divisible by

n

and, moreover, that

n

does not divide \sum^n_{i\equal{}1} a_i. Prove that there exist at least

n

different sequences

(e_1, e_2, \ldots, e_n)

consisting of zeros or ones such \sum^n_{i\equal{}1} e_i \cdot a_i is divisible by

n.

Problem Statement