\(S_p\)-Sets with Multiplier \(p\)

An \(S_h\)-set (mod \(m\)) is a set \(S\) of integers such that the sums\(a_1 + a_2 + \cdots + a_h\) of elements \(a_1 \leq a_2 \leq \cdots 1\) and prove that equality is possible at least when \(h=p\) is a prime (Theorem).