MathDB

n^2 divides sum of every n consecutive elements

Source: Baltic Way 2006

December 4, 2010

modular arithmeticinductionnumber theory proposednumber theory

Problem Statement

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