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^2-v^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 2018-12-09 08:50:52