摘要
We consider the congruence x1＋ x2 ＋… ＋ xr - c （mod m）, wherem and r are positive integers and c ∈Zm ：= {0, 1, ..., m- 1} （m ≥ 2）. Recently,W.-S. thou, T. X. He,and Peter J.-S. Shiue considered the enumerationproblems of this congruence, namely, the number of solutions with the restriction x1≤~ x2≤ ... ≤ xr, and got some properties and a neat formula ofthe solutions. Due to the lack of a simple computational method for calculating the number of the solution of the congruence, we provide an algebraic and a recursive algorithms for those numbers. The former one can also give a new and simple approach to derive some properties of solution numbers.
We consider the congruence x1＋ x2 ＋… ＋ xr - c （mod m）, wherem and r are positive integers and c ∈Zm ：= {0, 1, ..., m- 1} （m ≥ 2）. Recently,W.-S. thou, T. X. He,and Peter J.-S. Shiue considered the enumerationproblems of this congruence, namely, the number of solutions with the restriction x1≤~ x2≤ ... ≤ xr, and got some properties and a neat formula ofthe solutions. Due to the lack of a simple computational method for calculating the number of the solution of the congruence, we provide an algebraic and a recursive algorithms for those numbers. The former one can also give a new and simple approach to derive some properties of solution numbers.
