diophantine

Finding Integers With A Certain Property - Project Euler Problem 221

I've become very addicted to Project Euler recently and am trying to do this one next! I've started some analysis on it and have reduced the problem down substantially already. Here's my working: A = pqr and 1/A = 1/p + 1/q + 1/r so pqr/A = pq + pr + qr And because of the first equation: pq+pr+qr = 1 Since...

Project Euler Problem 233

I've decided to tackle Project Euler problem 233 next but I'm having some major problems! I've done some analysis and have made some quite nice progress but I've become stuck now. Here's my working: Lemma 1: Since the circle goes through the 4 corner points there are at least 4 solutions for any n. But for each point on the circumferenc...