Let G$G$ be an additive abelian group of size v$v$. A k$k$‐subset D$D$ of G$G$ is called a (v,k,λ)$(v, k, \lambda)$‐difference set if every non‐identity element in G$G$ can be written in λ$\lambda$ ways as the difference of two elements in D$D$. This letter proves the non‐existence of (pm,k,1)$(p^m, k, 1)$‐difference sets, for all prime p$p$ and m>1$m>1$.