8

Part of 1997 Moldova Team Selection Test

Problems(1)

there are $\frac{n(n+1)}{2}$ distinct remainders

Source: Moldova TST 1997

Find all integers

n>1

for which there exist positive integers

a_1,a_2,\ldots,a_n

such that when divided by

a_i+a_j, 1\leq i\leq j\leq n

\frac{n(n+1)}{2}

distinct remainders.