Further improvements of lower bounds for the least common multiples of arithmetic progressions

Authors:
Shaofang Hong and Scott Duke Kominers

Journal:
Proc. Amer. Math. Soc. **138** (2010), 809-813

MSC (2000):
Primary 11A05

DOI:
https://doi.org/10.1090/S0002-9939-09-10083-7

Published electronically:
September 4, 2009

MathSciNet review:
2566546

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Abstract | References | Similar Articles | Additional Information

Abstract: For relatively prime positive integers and , we consider the arithmetic progression .

Define and let be any integer. In this paper, we show that for integers and , we have

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Additional Information

**Shaofang Hong**

Affiliation:
Mathematical College, Sichuan University, Chengdu 610064, People’s Republic of China

Email:
sfhong@scu.edu.cn, s-f.hong@tom.com, hongsf02@yahoo.com

**Scott Duke Kominers**

Affiliation:
Department of Mathematics and Department of Economics, Harvard University, Cambridge, Massachusetts 02138

Address at time of publication:
Baker Library 420C, Harvard Business School, Soldiers Field, Boston, Massachusetts 02163

Email:
kominers@fas.harvard.edu, skominers@gmail.com

DOI:
https://doi.org/10.1090/S0002-9939-09-10083-7

Keywords:
Least common multiple,
arithmetic progression

Received by editor(s):
June 12, 2009

Published electronically:
September 4, 2009

Additional Notes:
The first author was partly supported by the National Science Foundation of China and by the Program for New Century Excellent Talents in University, Grant No. NCET-06-0785. The second author was partly supported by a U.S. National Science Foundation Graduate Research Fellowship and is the corresponding author.

Communicated by:
Wen-Ching Winnie Li

Article copyright:
© Copyright 2009
Shaofang Hong and Scott Duke Kominers