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Part of 2024 Taiwan TST Round 1

Problems(1)

partitioning 1 to p-1 into several a+b=c (mod p)

Source: own

4/21/2024
Given a prime number pp, a set is said to be pp-good if the set contains exactly three elements a,b,ca, b, c and a+b≡c(modp)a + b \equiv c \pmod{p}. Find all prime number pp such that {1,2,⋯ ,p−1}\{ 1, 2, \cdots, p-1 \} can be partitioned into several pp-good sets.
Proposed by capoouo
number theory