四川理工学院学报：自然科学版2011，Vol.24Issue(4)：389-392,4.
不定方程x~3＋y~3＋z~3-3xyz=n有非负整数解的充要条件
Sufficient and Necessary Condition for the Non-negative Integer Solution to Indefinite Equation x~3＋y~3＋z~3-3xyz=n
摘要
Abstract
A criterion of the non-negative integer solution is given to indefinite equation x3＋y3＋z3-3xyz=n.The main result is： If positive integer n has a standard decomposition n=2rpr11…prkk,where p1,p2,…,pk are odd primes satisfying that p1p2…pk,r,r1,r2,…,rk are positive integer,then a sufficient and necessary condition for the non-negative integer solution to the equation is p1≠3 or p1=3 with r1≥2.Thus a non-negative integer solution to this kind of indefinite equation is solved.关键词
不定方程/非负整数解/标准分解式/判定准则/充要条件Key words
indefinite equation/non-negative integer solution/standard decomposition/criterion/sufficient and necessary condition分类
数理科学引用本文复制引用
管训贵..不定方程x~3＋y~3＋z~3-3xyz=n有非负整数解的充要条件[J].四川理工学院学报：自然科学版,2011,24(4):389-392,4.基金项目
泰州师范高等专科学校重点课题资助项目 （）
