MathDB

M2558

Part of Kvant 2021

Problems(1)

Any number is divisible by the sum of the other numbers

Source: VI Caucasus Mathematical Olympiad

3/14/2021
We have n>2n>2 non-zero integers such that each one of them is divisible by the sum of the other nāˆ’1n-1 numbers. Prove that the sum of all the given numbers is zero.
number theory