19

Part of 2006 Baltic Way

Problems(1)

n^2 divides sum of every n consecutive elements

Source: Baltic Way 2006

Does there exist a sequence

a_1,a_2,a_3,\ldots

of positive integers such that the sum of every

n

consecutive elements is divisible by

n^2

for every positive integer

n

modular arithmeticinductionnumber theory proposednumber theory