All Pythagorean triples (or "triplets") are of this form:
(mē-nē, 2mn, mē+nē)
choose positive integers for m and n, but always choose a larger positive
integer for m than for n. Here are all the ones choosing integers
m and n as 10 or less:
m n mē-nē 2mn mē+nē triplet
-----------------------------------------
2 1 3 4 5 (3,4,5)
3 1 8 6 10 (8,6,10)
3 2 5 12 13 (5,12,13)
4 1 15 8 17 (15,8,17)
4 2 12 16 20 (12,16,20)
4 3 7 24 25 (7,24,25)
5 1 24 10 26 (24,10,26)
5 2 21 20 29 (21,20,29)
5 3 16 30 34 (16,30,34)
5 4 9 40 41 (9,40,41)
6 1 35 12 37 (35,12,37)
6 2 32 24 40 (32,24,40)
6 3 27 36 45 (27,36,45)
6 4 20 48 52 (20,48,52)
6 5 11 60 61 (11,60,61)
7 1 48 14 50 (48,14,50)
7 2 45 28 53 (45,28,53)
7 3 40 42 58 (40,42,58)
7 4 33 56 65 (33,56,65)
7 5 24 70 74 (24,70,74)
7 6 13 84 85 (13,84,85)
8 1 63 16 65 (63,16,65)
8 2 60 32 68 (60,32,68)
8 3 55 48 73 (55,48,73)
8 4 48 64 80 (48,64,80)
8 5 39 80 89 (39,80,89)
8 6 28 96 100 (28,96,100)
8 7 15 112 113 (15,112,113)
9 1 80 18 82 (80,18,82)
9 2 77 36 85 (77,36,85)
9 3 72 54 90 (72,54,90)
9 4 65 72 97 (65,72,97)
9 5 56 90 106 (56,90,106)
9 6 45 108 117 (45,108,117)
9 7 32 126 130 (32,126,130)
9 8 17 144 145 (17,144,145)
10 1 99 20 101 (99,20,101)
10 2 96 40 104 (96,40,104)
10 3 91 60 109 (91,60,109)
10 4 84 80 116 (84,80,116)
10 5 75 100 125 (75,100,125)
10 6 64 120 136 (64,120,136)
10 7 51 140 149 (51,140,149)
10 8 36 160 164 (36,160,164)
10 9 19 180 181 (19,180,181)
Edwin
