Proposition: Number of Multiples of a Given Number Less Than Another Number

Let $0 < n < m$ be natural numbers. The number $k$ of the positive multiples of $n$ below $m,$ i.e. the numbers $n, 2n, 3n,\ldots,kn$ with $kn\le m$ is given by the floor function $k=\left\lfloor \frac mn\right\rfloor.$

Proofs: 1

Proofs: 1 2 3

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  1. Scheid Harald: "Zahlentheorie", Spektrum Akademischer Verlag, 2003, 3rd Edition
  2. Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927