关于 m,n 的方程 m/n=n.m 除 (m,n)=(5,2) 外是否有其他正整数解？

H2L

请教一下

王守恩

Solve[{m/n == n + m/10, m > 0, n > 0}, {m, n}, Integers]
{{5, 2}, {50, 5}, {90, 6}, {320, 8}, {810, 9}}

Solve[{m/n == n + m/10, m > 0, n < 0}, {m, n}, Integers]
{{50, -10}, {90, -15}, {225, -30}, {320, -40}, {810, -90},
{1058, -115}, {1805, -190}, {2304, -240}, {4802, -490}, {9801, -990}}

Solve[{m/n == n + m/10, m < 0, n > 0}, {m, n}, Integers]
{{-10201, 1010}, {-5202, 510}, {-2704, 260}, {-2205, 210}, {-1458, 135},
{-1210, 11}, {-1210, 110}, {-720, 12}, {-720, 60}, {-625, 50}, {-490, 14},
{-490, 35}, {-450, 15}, {-450, 30}, {-405, 18}, {-400, 20}}

Solve[{m/n == n + m/10, m < 0, n < 0}, {m, n}, Integers]
{}

Solve[{m/n == n + m/100, m > 0, n > 0}, {m, n}, Integers]
{{500, 20}, {2025, 36}, {5000, 50}, {9000, 60}, {14450, 68},
{22500, 75}, {32000, 80}, {44100, 84}, {81000, 90}, {105800, 92},
{180500, 95}, {230400, 96}, {480200, 98}, {980100, 99}}