Bosnia and Herzegovina JBMO TST 2013 Problem 1
Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2013
September 16, 2018
number theorySum of Squaresdivisible
Problem Statement
It is given positive integers. Product of any one of them with sum of remaining numbers increased by is divisible with sum of all numbers. Prove that sum of squares of all numbers is divisible with sum of all numbers