Still Unfinished
27th to solve P-Euler problem 140 :)
so, i've been using the method i discovered in the last post to solve the past four new problems, which all simplified to the concept of "given some quadratic equation in x, find all the values of x for which the result is a perfect square."
and the sequence of solutions always grows exponentially, and i realized that i can always generate a recursive function for the sequence of solutions in the form of x_n = ax_(n-1) - x_(n-2) + b. All it takes is a little notepad arithmetic guess-and-check.
I still don't know why it works, and there's a part of me that gets annoyed every time i apply it to solve a problem because i really shouldn't be using anything in math that i don't understand. i need to take time off and figure this out. hopefully before the next new problem on P-Euler comes out.
so, i've been using the method i discovered in the last post to solve the past four new problems, which all simplified to the concept of "given some quadratic equation in x, find all the values of x for which the result is a perfect square."
and the sequence of solutions always grows exponentially, and i realized that i can always generate a recursive function for the sequence of solutions in the form of x_n = ax_(n-1) - x_(n-2) + b. All it takes is a little notepad arithmetic guess-and-check.
I still don't know why it works, and there's a part of me that gets annoyed every time i apply it to solve a problem because i really shouldn't be using anything in math that i don't understand. i need to take time off and figure this out. hopefully before the next new problem on P-Euler comes out.