Disjoint odd integer subsets having a constant even sum Original Research Article

We prove that for positive integers n and k and a positive even integer m, the odd integer set 1, 3, 5, …, 2n−1 contains k disjoint subsets having a constant sum m if and only if 4k⩽m⩽n2/k, n2−mk≠4n−2 or n≠4k.