4

Part of 1993 Bulgaria National Olympiad

Problems(1)

a_n such that {a_i +a_j} form a full system modulo n(n+1)/2

Source: 1993 Bulgaria NMO, Round 4, p4

Find all natural numbers

n > 1

for which there exists such natural numbers

a_1,a_2,...,a_n

for which the numbers

\{a_i +a_j | 1 \le i \le j \le n \}

form a full system modulo

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