Upside down Diophantine equation
Upside Down is a modification of the famous Pythagorean equation:
A solution to this equation with and positive integers is a primitive solution if .
Let be the sum of over primitive Upside Down solutions such that and .
For the primitive solutions are and , thus .
It can be checked that and .
Find and give the last digits as your answer.
颠倒不定方程
把著名的毕达哥拉斯方程稍加修改就得到了如下的颠倒不定方程:
若上述方程的一组正整数解满足,则称之为该方程的本原解。
考虑该方程的所有本原解,并记为所有满足和的本原解对应之和。
对于,满足条件的本原解包括和,因此。
可以验证,,。
求,并给出最后位数字作为你的答案。
Gitalking ...