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不少计数问题归结为不定方程 x1+ x2+… + xn =m在特定条件下的解的个数问题便迎刃而解 .本文研究不定方程 x1+ x2 +… + xn =m在有关条件下的解的个数问题 ,并举例说明其在计数问题中的应用 .(注 :文中约定 :当 m n时 Cnm =0 ) .结论 1 方程 x1+ x2 +… + xn =m ( n,m∈ N
Many counting problems boil down to the indefinite equation x1+ x2+... + xn = m The number of solutions under certain conditions solves the problem. This paper studies the number of solutions of the indefinite equation x1+ x2 +... + xn = m under relevant conditions. , and illustrate its application in the counting problem. (Note: In the text, Cnm = 0 when mn). Conclusion 1 Equation x1+ x2 +... + xn = m ( n,m∈ N