Enumeration Problems for a Linear Congruence Equation

Tian-Xiao He, Wun-Seng Chou, Peter J. Shiue

Research output: Journal ArticleArticlepeer-review

Abstract

<div class="line" id="line-5"> Let m &ge; 2 and r &ge; 1 be integers and let c &Jukcy; Zm = {0, 1, &hellip;,m &boxh; 1}. In this paper, we give an upper bound and a lower bound for the number of unordered solutions x1, &hellip;, xn &Jukcy; Zm of the congruence x1 + x2 + &bull;&bull;&bull; + xr &equiv; c mod m. Exact formulae are also given when m or r is prime. This solution number involves the Catalan number or generalized Catalan number in some special cases. Moreover, the enumeration problem has interrelationship with the restricted integer partition.</div>
Original languageAmerican English
JournalTaiwanese Journal of Mathematics
Volume18
DOIs
StatePublished - Feb 2014

Keywords

  • Congruence
  • Catalan number
  • generalized Catalan number
  • integer partition

Disciplines

  • Mathematics

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