一类线性不定方程的非负整数解组数

The Number of Nonnegative Integeral Resolution of a Class of Indeterminate Equation

不定方程是数论的一个分支.所谓不定方程是指解的范围为整数、正整数、有理数或代数整数的方程或方程组,其未知数的个数通常多于方程的个数.在实际的应用中,不定方程的非负整数解组数备受人们的关注.通过讨论2个参数较小的线性不定方程的非负整数解的个数,给出了形如x+ky+(k+1)z=n的一类不定方程的非负整数解组的个数.

As a branch of the theory of numbers,the indeterminate equation is an equation whose solution can be integer, positive integer, rational number or algebraic integer. In practical applications, the number of non - negative integeral solution of indeterminate equation is often paid great attention to. According to the discussion of the two indeterminate equations with small parameters,the number of non negative integeral solution of indeterminate equation like the form of x ＋ ky＋ （ k ＋ 1 ）x = n is found. The number of nonneyative integeral solution of indeterminate equation like the form of x ＋ky ＋ （k ＋ 1 ）z = n is found according to the discussion of the two indeter minate equation with small parameters.