MathDB

Let

k

be a positive integer and

a_1, a_2,... , a_k

be nonnegative real numbers. Initially, there is a sequence of

n \geq k

zeros written on a blackboard. At each step, Nicole chooses

k

consecutive numbers written on the blackboard and increases the first number by

a_1

, the second one by

a_2

, and so on, until she increases the

k

-th one by

a_k

. After a positive number of steps, Nicole managed to make all the numbers on the blackboard equal. Prove that all the nonzero numbers among

a_1, a_2, . . . , a_k

are equal.

Problem Statement