摘要
设m≠0为给定整数.本文证明:1) m可真表示为两个幂数之差,其中前一个幂数为完全平方数,并且表法无穷.2) m可表示为两个非完全平方数的幂数之差,且表法无穷;当m不是16的倍数时、m可真表示为两个非完全平方数的幂数之差,而表法无穷.
We prove following theorems: Th.A.If m=0 is a given integer, then m have infinitely many proper representations of the diff erencs between two powerful numbers and the former powerful number is a perfect square. Th.B. If m is a given integer,then m have infinitely many representations of the difference between two non-Square powerful numbers. Furthermore, if m is riot the multiplicity of 16, then m have infinitely many proper representations of the difference between two nonsquare powerful numbers.
出处
《四川大学学报（自然科学版）》
CAS
CSCD
1989年第3期277-282,共6页
Journal of Sichuan University(Natural Science Edition)
基金
国家自然科学基金资助项目
关键词
Pell方差
刁番图方程
幂数差
Pell equation, Diophantine equation, powerful number difference, perfect square, proper representation.
