关于Murthy问题的解

On the solutions of Murthy problem

对于适合a<b的正整数a和b,如果∑b i-a i=ab,则称(a,b)是一对友好数。运用Pell方程x2-2y2=±1的解序列的递归性,得到了方程∑b i-a i=ab的全部正整数解,从而给出了所有的友好数对。

For positive integers a and b with a 〈 b, ∑1=a^bi=ab, then （a,b） is called a friendly number pair. b i=a All positive integer solutions to the equation ∑1=a^bi=ab is proposed in this issue by using the reeursive property of i=a solution sequence of the Pell equations x^2 - 2y^2 = ＋1. Additionary, all friendly number pairs are given.