%0 Journal Article
%T 丢番图方程ax+by=n的一个注记（英文）
%A 薛晓果
%A 孟倩倩
%A 张　彬
%A 任福梅
%J 南京师范大学学报(自然科学版)
%D 2015
%X 令[a,b]为互素的正整数，[n]为非负整数. [D(a,b;n)]表示不定方程[ax+by=n]的非负整数解[(x,y)]的个数. Tripathi证明了[D(a,b;n)=nab+121a+1b+1aj=1a-1ζ-jna1-ζbja+1bk=1b-1ζ-knb1-ζakb]，其中[ζm=e2πi/m]. 在本文中，我们建立了[D(a,b;n)]的递推关系，从而给出了上述结论的新证明.</br>Let a，b be positive integers such that（a，b）=1 and let n be a non-negative integer. Define [D(a,b;n)] to be the number of non-negative integer solutions（x，y）of the Diophantine equation ax+by=n. Tripathi proved that[D(a,b;n)=nab+121a+1b+1aj=1a-1ζ-jna1-ζbja+1bk=1b-1ζ-knb1-ζakb]，where [ζm=e2πi/m]. In this note，we put forward a recurrence relation of [D(a,b;n)]，thus giving a new proof of above formula
%K 丢番图方程
%K 生成函数
%K 留数定理&lt
%K /br&gt
%K Diophantine equation
%K generating function
%K Residue theorem
%U http://njsfdxzrb.paperonce.org/oa/darticle.aspx?type=view&id=201504006