Tool to generate Pythagorean triples. A Pythagorean triple is a set of three natural numbers a, b, and c, such that a^2+b^2=c^2, for example (3,4,5) is a Triple of Pythagore: 3^2+4^2=5^2

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Tool to generate Pythagorean triples. A Pythagorean triple is a set of three natural numbers a, b, and c, such that a^2+b^2=c^2, for example (3,4,5) is a Triple of Pythagore: 3^2+4^2=5^2

Answers to Questions

How to find a Pythagorean Triple?

It exists heuristics but the simple method consists in testing iteratively all possibilities of a and b when s is given, the value of c is constrained by s=a+b+c.

$$ a^2 + b^2 = (s − a − b)^2 $$

$$ a <= (s − 3)/3 $$

$$ b < (s − a)/2 $$

What is the list of Pythagorean Triples?

The first Pythagorean triples (side inferior to 100)

3,4,5

5,12,13

6,8,10

7,24,25

8,15,17

9,12,15

9,40,41

10,24,26

11,60,61

12,16,20

12,35,37

13,84,85

14,48,50

15,20,25

15,36,39

16,30,34

16,63,65

18,24,30

18,80,82

20,21,29

20,48,52

21,28,35

21,72,75

24,32,40

24,45,51

24,70,74

25,60,65

27,36,45

28,45,53

28,96,100

30,40,50

30,72,78

32,60,68

33,44,55

33,56,65

35,84,91

36,48,60

36,77,85

39,52,65

39,80,89

40,42,58

40,75,85

42,56,70

45,60,75

48,55,73

48,64,80

51,68,85

54,72,90

57,76,95

60,63,87

60,80,100

65,72,97

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