If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.
{20,48,52}, {24,45,51}, {30,40,50}
For which value of p ≤ 1000, is the number of solutions maximized?
Source: Project Euler
(In reply to
trying to understand... by Steven Lord)
Sure, Steven:
My point was that (u^2v^2), (u^2+v^2) and 2uv are the generalised side lengths of every right triangle, so the perimeter of every such triangle must simply be their sum, which is 2u(u+v).
So the problem should be equivalent to asking which numbers have the record number of divisors.
All that said, A099830 comfirms your findings, so the correlation is not as strict as I assumed.
Edited on December 9, 2018, 9:11 am

Posted by broll
on 20181209 08:50:52 