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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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trying to understand... | Comment 3 of 5 |
(In reply to Another method by broll)

1st: Could you please explain your formula a little? Is a=(u-v) and b=(u+b). Even if so, I do not follow - thanks!


2nd: the correspondence with A002182 is not strict:

If you compare the number of solutions for record holding perimeters, or record breaking perimeter values, neither list  strictly follow A002182.

record holders

    # of equal perimeters    perimeters

           1          12

           1          24

           1          30

           1          36

           1          40

           1          48

           1          56

           2          60

           2          84

           2          90

           3         120

           3         168

           3         180

           4         240

           4         360

           5         420

           5         660

           6         720

           8         840

           8        1260

          10        1680

          12        2520

          13        4620

          16        5040

          20        9240

          29       11969





or record breakers


                      2          60

           3         120

           4         240

           5         420

           6         720

           8         840

          10        1680

          12        2520

          13        4620

          16        5040

          20        9240

          29       11969

 

A002182:


…, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560, 10080, 15120

Thanks!

SL

(ps - I hope I have these right - I must still check further.)


Edited on December 9, 2018, 4:00 am
  Posted by Steven Lord on 2018-12-09 04:00:02

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