A result on Ma's conjecture (Q1906131)

With only one exception, all known difference sets admitting \(-1\) as a multiplier are Hadamard difference sets: The exceptional example is a (4000, 775, 125)-difference set. It is conjectured that this is the only non-Hadamard difference set with multiplier \(-1\). \textit{S. L. Ma} [Des. Codes Cryptography 1, No. 4, 321-332 (1991; Zbl 0758.05028)] has shown that this conjecture is equivalent to a number theoretic condition. In this short note, the authors prove part of this condition. The proof uses only elementary number theory.