For \(n\geq 1\), let \(B_ n(t)\) denote the \(n\)-th Bernoulli polynomial. \textit{G. Almkvist} and \textit{A. Meurman} [C. R. Math. Acad. Sci., Soc. R. Can. 13, No. 2/3, 104-108 (1991; Zbl 0731.11014)] proved that \(B_ n(h/k)- B_ n(0)\in (1/k^ n)\mathbb{Z}\) whenever \(h\) and \(k\) are positive integers. The author proves this in a shorter way.