Given any integer n≥2, assume that the integers a1,a2,…,an 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 (e1,e2,…,en) consisting of zeros or ones such \sum^n_{i\equal{}1} e_i \cdot a_i is divisible by n. algebraDivisibilitySequenceIMO Shortlist