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Maximal number of solutions (Posted on 2018-12-08) Difficulty: 4 of 5
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

See The Solution Submitted by Ady TZIDON    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re: trying to understand... | Comment 4 of 5 |
(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

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