MathDB

Let

\{x_i\}, 1\le i\le 6

be a given set of six integers, none of which are divisible by

7

(a)

Prove that at least one of the expressions of the form

x_1\pm x_2\pm x_3\pm x_4\pm x_5\pm x_6

is divisible by

7

, where the

\pm

signs are independent of each other.

(b)

Generalize the result to every prime number.

12