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 Maximal number of solutions (Posted on 2018-12-08)
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 No Rating

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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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