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A Sum of Reciprocals of Least Common Multiples

Published online by Cambridge University Press:  20 November 2018

D. Borwein
D. Borwein*
Affiliation:
The University of Western Ontario, London, Ontario, Canada N6A 5B9
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The purpose of this note is to prove the following theorem conjectured by P. Erdös.

Theorem. Let a0, a1, …, ak be integers satisfying 1 ≤ a0 a1 … k, and let [ai-1 ai] denote the least common multiple of ai-1 and ai Then

1

with equality occurring if and only if ai = 2i for 1 ≤ i ≤ k.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 1 , 01 March 1978 , pp. 117 - 118
Copyright
Copyright © Canadian Mathematical Society 1978