【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.更多还原

【Abstract】 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.更多还原