Enumeration Problems for a Linear Congruence Equation
Publication Date
February 2014
Abstract
Let m ≥ 2 and r ≥ 1 be integers and let c Є Zm = {0, 1, …,m ─ 1}. In this paper, we give an upper bound and a lower bound for the number of unordered solutions x1, …, xn Є Zm of the congruence x1 + x2 + ••• + xr ≡ 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.
Disciplines
Mathematics
Recommended Citation
He, Tian-Xiao; Chou, Wun-Seng; and Shiue, Peter, "Enumeration Problems for a Linear Congruence Equation" (2014). Scholarship. 2.
https://digitalcommons.iwu.edu/math_scholarship/2
COinS
Comments
The Taiwanese Journal of Mathematics, is published by the Mathematical Society of the Republic of China, http://journal.taiwanmathsoc.org.tw/index.php/TJM/index.