IMO 1970 LL BUL12

Let x1, x2, x3, x4, x5, x6 be given integers, not divisible by 7.

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IMO 1970 LL BUL12

Origin: BUL

Problem

Let x1, x2, x3, x4, x5, x6 be given integers, not divisible by 7. Prove that at least one of the expressions of the form \pmx1 \pm x2 \pm x3 \pm x4 \pm x5 \pm x6 is divisible by 7, where the signs are selected in all possible ways. (Gener- alize the statement to every prime number!)