Restrictions upon multipliers of an Abelian difference set (Q1110519)

It is pointed out that some ``new'' results are improved by an old theorem proved using algebraic number theory and (in 1983) using group representations: usually a multiplier of an Abelian set of an Abelian group G with exponent e has an odd order (mod e). From this: Let p be a prime divisor of \(n=k-\lambda\). For \(F(v,k)=1\) and n a non-square if p is a multiplier of a (v,k,\(\lambda)\)-difference set in an Abelian group, then p is a square (mod v). The link is simple but not trivial.