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THE LEAST COMMON MULTIPLE OF CONSECUTIVE TERMS IN A QUADRATIC PROGRESSION

Published online by Cambridge University Press:  12 April 2012

GUOYOU QIAN
Affiliation:
Mathematical College, Sichuan University, Chengdu 610064, PR China (email: [email protected], [email protected])
QIANRONG TAN
Affiliation:
School of Computer Science and Technology, Panzhihua University, Panzhihua 617000, PR China (email: [email protected])
SHAOFANG HONG*
Affiliation:
Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, PR China (email: [email protected], [email protected], [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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Let k be any given positive integer. We define the arithmetic function gk for any positive integer n by We first show that gk is periodic. Subsequently, we provide a detailed local analysis of the periodic function gk, and determine its smallest period. We also obtain an asymptotic formula for log lcm0≤ik {(n+i)2+1}.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

S. Hong was supported partially by National Science Foundation of China Grant #10971145 and by the PhD Programs Foundation of Ministry of Education of China Grant #20100181110073.

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