摘要
利用正整数n的一类特殊的3分拆n=n1+n2+n3,n1>n2>n3≥1,且n2+n3>n1的Ferrers图将不定方程4x1+3x2+2x3=n(n≥9)的正整数解与这种分拆联系起来,从而得到了该不定方程的正整数解数公式;同时也给出了正整数n的一类4分拆的计数公式.此外,还给出了周长为n的整边三角形的计数公式的一个简单证明.
We give a relation for the positive integer solution of Diophantine equation 4x1＋3x2＋2x3=n（n≥9） and the partition with 3 parts by Ferrers graph of this partition. So we got the counting formula of number of positive integer solution of Diophantine equation 4x1＋3x2＋2x3=n（n≥9）. And we also got a counting formula for number of a kind of partition with 4 parts of integer n. Moreover, the simple proof for the counting formula of number for triangle with integer sides which has perimeter n is given.
出处
《大学数学》
北大核心
2006年第3期111-114,共4页
College Mathematics
