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Sum of n numbers is 0 when each is divisible by other’s sum

Source: 2021 Saudi Arabia JBMO TST 2.3

September 4, 2021
number theorydivisibledivides

Problem Statement

We have n>2n > 2 nonzero integers such that everyone of them is divisible by the sum of the other nāˆ’1n - 1 numbers, Show that the sum of the nn numbers is precisely 00.
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