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Proof pearl: Bounding least common multiples with triangles

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Date

2016

Authors

Chan, Hing Lun
Norrish, Michael

Journal Title

Journal ISSN

Volume Title

Publisher

Springer International Publishing Switzerland

Abstract

We present a proof of the fact that 2n ≤ lcm{1, 2, 3, …, (n+1)}. This result has a standard proof via an integral, but our proof is purely number theoretic, requiring little more than list inductions. The proof is based on manipulations of a variant of Leibniz’s Harmonic Triangle, itself a relative of Pascal’s better-known Triangle.

Description

Keywords

Citation

URI

http://hdl.handle.net/1885/317544

Collections

ANU Research Publications

Source

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Type

Conference paper

Book Title

Entity type

Access Statement

License Rights

DOI

10.1007/978-3-319-43144-4_9

Restricted until

2099-12-31

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Description
Proof Pearl.pdf (412.26 KB)

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