project euler problem 421

Prime factors of n¹⁵+1

I am very happy that this problem is solved.  Although my solution is not as elegant as those guys who solved it in a couple of hours after the problem was posted. But it is not too bad. It takes 23 seconds to get the answer. 

I do not know how to solve this problem after I read the problem. Although I knew how to do the factorization of n¹⁵+1(polynomial), but it is useless. The numbers are huge! Then, I found some old problems are closely related to this problem, i.e., problem 271 and 272. I reviewed the discussion of these two problems and found some real gems in the discussion! It really helps to solve the problem! 

I really believe reading the discussion of a problem is as important as solving a problem by oneself. In some sense, it is even more important than solving  a problem. A lot of genius gave incisive comments in the discussion that we may benefit from.