Proof Pearl: Bounding Least Common Multiples with Triangles

Chan, Hing Lun Joseph; Norrish, Michael

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Proof Pearl: Bounding Least Common Multiples with Triangles

Date

2017

Authors

Chan, Hing Lun Joseph

Norrish, Michael

Publisher

Kluwer Academic Publishers

Abstract

We present a proof of the fact that Open image in new window for \(n \ge 0\). This result has a standard proof via an integral, but our proof is purely number-theoretic, requiring little more than inductions based on lists. The almost-pictorial proof is based on manipulations of a variant of Leibniz’s harmonic triangle, itself a relative of Pascal’s better-known Triangle.