Disjoint odd integer subsets having a constant odd sum (Q1322179)

\textit{K. Ando}, \textit{S. Gervacio} and \textit{M. Kano} [Discrete Math. 82, No. 1, 7-11 (1990; Zbl 0732.05002)] characterized for positive integers \(n\), \(m\), \(k\), systems of \(k\) disjoint nonempty subsets of \(\{1,2, \dots, n\}\) having constant sum \(m\). They also conjectured a characterization of a similar result for \(k\) disjoint nonempty subsets of \(\{1,3,5, \dots, 2n-1\}\). This conjecture was in two parts, according as \(m\) is even or odd. Ando, Gervacio, and Kano announced the even case of their conjecture had been proved by H. Enomoto and M. Kano. The present paper contains a proof of the conjecture when \(m\) is odd.