## Two Pythagorean triangles with Equal Sums (or differences) of legs

Find other pairs.

math grad - Interest: Number theory
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### 1 Response to Two Pythagorean triangles with Equal Sums (or differences) of legs

1. Paul says:

and some more

{{9,40,41},{21,28,35}} , 9 + 40 = 21 + 28 = 49
{{17,144,145},{44,117,125}} , 17 + 144 = 44 + 117 = 161
{{17,144,145},{56,105,119}} , 17 + 144 = 56 + 105 = 161
{{17,144,145},{69,92,115}} , 17 + 144 = 69 + 92 = 161
{{18,80,82},{42,56,70}} , 18 + 80 = 42 + 56 = 98
{{20,99,101},{35,84,91}} , 20 + 99 = 35 + 84 = 119
{{20,99,101},{39,80,89}} , 20 + 99 = 39 + 80 = 119
{{20,99,101},{51,68,85}} , 20 + 99 = 51 + 68 = 119
{{23,264,265},{32,255,257}} , 23 + 264 = 32 + 255 = 287
{{27,120,123},{63,84,105}} , 27 + 120 = 63 + 84 = 147
{{34,288,290},{88,234,250}} , 34 + 288 = 88 + 234 = 322
{{35,84,91},{39,80,89}} , 35 + 84 = 39 + 80 = 119
{{35,84,91},{51,68,85}} , 35 + 84 = 51 + 68 = 119
{{36,160,164},{84,112,140}} , 36 + 160 = 84 + 112 = 196
{{37,684,685},{100,621,629}} , 37 + 684 = 100 + 621 = 721
{{39,80,89},{51,68,85}} , 39 + 80 = 51 + 68 = 119
{{40,198,202},{70,168,182}} , 40 + 198 = 70 + 168 = 238
{{40,198,202},{78,160,178}} , 40 + 198 = 78 + 160 = 238
{{44,117,125},{56,105,119}} , 44 + 117 = 56 + 105 = 161
{{44,117,125},{69,92,115}} , 44 + 117 = 69 + 92 = 161
{{46,528,530},{64,510,514}} , 46 + 528 = 64 + 510 = 574
{{49,168,175},{52,165,173}} , 49 + 168 = 52 + 165 = 217
{{49,168,175},{85,132,157}} , 49 + 168 = 85 + 132 = 217
{{49,168,175},{93,124,155}} , 49 + 168 = 93 + 124 = 217
{{52,165,173},{85,132,157}} , 52 + 165 = 85 + 132 = 217
{{52,165,173},{93,124,155}} , 52 + 165 = 93 + 124 = 217
{{56,105,119},{69,92,115}} , 56 + 105 = 69 + 92 = 161
{{63,280,287},{96,247,265}} , 63 + 280 = 96 + 247 = 343
{{69,260,269},{84,245,259}} , 69 + 260 = 84 + 245 = 329
{{69,792,795},{96,765,771}} , 69 + 792 = 96 + 765 = 861
{{70,168,182},{78,160,178}} , 70 + 168 = 78 + 160 = 238
{{85,132,157},{93,124,155}} , 85 + 132 = 93 + 124 = 217

and

{{5,12,13},{8,15,17}} , 12 – 5 = 15 – 8 = 7
{{5,12,13},{21,28,35}} , 12 – 5 = 28 – 21 = 7
{{5,12,13},{48,55,73}} , 12 – 5 = 55 – 48 = 7
{{5,12,13},{65,72,97}} , 12 – 5 = 72 – 65 = 7
{{6,8,10},{40,42,58}} , 8 – 6 = 42 – 40 = 2
{{7,24,25},{28,45,53}} , 24 – 7 = 45 – 28 = 17
{{7,24,25},{51,68,85}} , 24 – 7 = 68 – 51 = 17
{{7,24,25},{88,105,137}} , 24 – 7 = 105 – 88 = 17
{{8,15,17},{21,28,35}} , 15 – 8 = 28 – 21 = 7
{{8,15,17},{48,55,73}} , 15 – 8 = 55 – 48 = 7
{{8,15,17},{65,72,97}} , 15 – 8 = 72 – 65 = 7
{{9,12,15},{60,63,87}} , 12 – 9 = 63 – 60 = 3
{{9,40,41},{60,91,109}} , 40 – 9 = 91 – 60 = 31
{{9,40,41},{93,124,155}} , 40 – 9 = 124 – 93 = 31
{{10,24,26},{16,30,34}} , 24 – 10 = 30 – 16 = 14
{{10,24,26},{42,56,70}} , 24 – 10 = 56 – 42 = 14
{{10,24,26},{96,110,146}} , 24 – 10 = 110 – 96 = 14
{{11,60,61},{35,84,91}} , 60 – 11 = 84 – 35 = 49
{{11,60,61},{56,105,119}} , 60 – 11 = 105 – 56 = 49
{{12,16,20},{80,84,116}} , 16 – 12 = 84 – 80 = 4
{{12,35,37},{33,56,65}} , 35 – 12 = 56 – 33 = 23
{{12,35,37},{69,92,115}} , 35 – 12 = 92 – 69 = 23
{{14,48,50},{56,90,106}} , 48 – 14 = 90 – 56 = 34
{{15,20,25},{100,105,145}} , 20 – 15 = 105 – 100 = 5
{{15,36,39},{24,45,51}} , 36 – 15 = 45 – 24 = 21
{{15,36,39},{63,84,105}} , 36 – 15 = 84 – 63 = 21
{{16,30,34},{42,56,70}} , 30 – 16 = 56 – 42 = 14
{{16,30,34},{96,110,146}} , 30 – 16 = 110 – 96 = 14
{{16,63,65},{85,132,157}} , 63 – 16 = 132 – 85 = 47
{{19,180,181},{60,221,229}} , 180 – 19 = 221 – 60 = 161
{{19,180,181},{84,245,259}} , 180 – 19 = 245 – 84 = 161
{{20,48,52},{32,60,68}} , 48 – 20 = 60 – 32 = 28
{{20,48,52},{84,112,140}} , 48 – 20 = 112 – 84 = 28
{{21,28,35},{48,55,73}} , 28 – 21 = 55 – 48 = 7
{{21,28,35},{65,72,97}} , 28 – 21 = 72 – 65 = 7
{{21,72,75},{84,135,159}} , 72 – 21 = 135 – 84 = 51
{{22,120,122},{70,168,182}} , 120 – 22 = 168 – 70 = 98
{{24,45,51},{63,84,105}} , 45 – 24 = 84 – 63 = 21
{{24,70,74},{66,112,130}} , 70 – 24 = 112 – 66 = 46
{{24,143,145},{49,168,175}} , 143 – 24 = 168 – 49 = 119
{{24,143,145},{57,176,185}} , 143 – 24 = 176 – 57 = 119
{{24,143,145},{85,204,221}} , 143 – 24 = 204 – 85 = 119
{{25,60,65},{40,75,85}} , 60 – 25 = 75 – 40 = 35
{{25,312,313},{36,323,325}} , 312 – 25 = 323 – 36 = 287
{{28,45,53},{51,68,85}} , 45 – 28 = 68 – 51 = 17
{{28,45,53},{88,105,137}} , 45 – 28 = 105 – 88 = 17
{{30,72,78},{48,90,102}} , 72 – 30 = 90 – 48 = 42
{{32,60,68},{84,112,140}} , 60 – 32 = 112 – 84 = 28
{{33,56,65},{69,92,115}} , 56 – 33 = 92 – 69 = 23
{{35,84,91},{56,105,119}} , 84 – 35 = 105 – 56 = 49
{{36,77,85},{39,80,89}} , 77 – 36 = 80 – 39 = 41
{{36,105,111},{99,168,195}} , 105 – 36 = 168 – 99 = 69
{{40,96,104},{64,120,136}} , 96 – 40 = 120 – 64 = 56
{{42,56,70},{96,110,146}} , 56 – 42 = 110 – 96 = 14
{{44,117,125},{95,168,193}} , 117 – 44 = 168 – 95 = 73
{{45,108,117},{72,135,153}} , 108 – 45 = 135 – 72 = 63
{{48,55,73},{65,72,97}} , 55 – 48 = 72 – 65 = 7
{{48,286,290},{98,336,350}} , 286 – 48 = 336 – 98 = 238
{{49,168,175},{57,176,185}} , 168 – 49 = 176 – 57 = 119
{{49,168,175},{85,204,221}} , 168 – 49 = 204 – 85 = 119
{{50,120,130},{80,150,170}} , 120 – 50 = 150 – 80 = 70
{{50,624,626},{72,646,650}} , 624 – 50 = 646 – 72 = 574
{{51,68,85},{88,105,137}} , 68 – 51 = 105 – 88 = 17
{{55,132,143},{88,165,187}} , 132 – 55 = 165 – 88 = 77
{{57,176,185},{85,204,221}} , 176 – 57 = 204 – 85 = 119
{{60,91,109},{93,124,155}} , 91 – 60 = 124 – 93 = 31
{{60,144,156},{96,180,204}} , 144 – 60 = 180 – 96 = 84
{{60,221,229},{84,245,259}} , 221 – 60 = 245 – 84 = 161
{{63,280,287},{68,285,293}} , 280 – 63 = 285 – 68 = 217
{{72,154,170},{78,160,178}} , 154 – 72 = 160 – 78 = 82

Paul.