MathDB

1

Part of 2013 Bosnia and Herzegovina Junior BMO TST

Problems(1)

Bosnia and Herzegovina JBMO TST 2013 Problem 1

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2013

9/16/2018
It is given nn positive integers. Product of any one of them with sum of remaining numbers increased by 11 is divisible with sum of all nn numbers. Prove that sum of squares of all nn numbers is divisible with sum of all nn numbers
number theorySum of Squaresdivisible