# SOLUTION: Pythagorean triplets represent a special relation that both satisfy the Pythagorean theorem and as well as another characteristic. It is this additional characteristic that I am es

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 Click here to see ALL problems on Pythagorean-theorem Question 275017: Pythagorean triplets represent a special relation that both satisfy the Pythagorean theorem and as well as another characteristic. It is this additional characteristic that I am especially looking for. There are several formulas that will produce Pythagorean triplets. I need to find at least one. I need at least 5 other examples of triplets, not including 3-4-5. Found 2 solutions by Edwin McCravy, Alan3354:Answer by Edwin McCravy(8908)   (Show Source): You can put this solution on YOUR website!Pythagorean triplets represent a special relation that both satisfy the Pythagorean theorem and as well as another characteristic. It is this additional characteristic that I am especially looking for. There are several formulas that will produce Pythagorean triplets. I need to find at least one. I need at least 5 other examples of triplets, not including 3-4-5. ``` One formula is where you can substitute any positive integers for and . if k = 1 and q = 1 then we have a = 3, b = 4; and c = 5 if k = 1 and q = 2 then we have a = 5, b = 12; and c = 13 if k = 1 and q = 3 then we have a = 7, b = 24; and c = 25 if k = 1 and q = 4 then we have a = 9, b = 40; and c = 41 if k = 1 and q = 5 then we have a = 11, b = 60; and c = 61 if k = 1 and q = 6 then we have a = 13, b = 84; and c = 85 if k = 1 and q = 7 then we have a = 15, b = 112; and c = 113 if k = 1 and q = 8 then we have a = 17, b = 144; and c = 145 if k = 1 and q = 9 then we have a = 19, b = 180; and c = 181 if k = 1 and q = 10 then we have a = 21, b = 220; and c = 221 if k = 2 and q = 1 then we have a = 8, b = 6; and c = 10 if k = 2 and q = 2 then we have a = 12, b = 16; and c = 20 if k = 2 and q = 3 then we have a = 16, b = 30; and c = 34 if k = 2 and q = 4 then we have a = 20, b = 48; and c = 52 if k = 2 and q = 5 then we have a = 24, b = 70; and c = 74 if k = 2 and q = 6 then we have a = 28, b = 96; and c = 100 if k = 2 and q = 7 then we have a = 32, b = 126; and c = 130 if k = 2 and q = 8 then we have a = 36, b = 160; and c = 164 if k = 2 and q = 9 then we have a = 40, b = 198; and c = 202 if k = 2 and q = 10 then we have a = 44, b = 240; and c = 244 if k = 3 and q = 1 then we have a = 15, b = 8; and c = 17 if k = 3 and q = 2 then we have a = 21, b = 20; and c = 29 if k = 3 and q = 3 then we have a = 27, b = 36; and c = 45 if k = 3 and q = 4 then we have a = 33, b = 56; and c = 65 if k = 3 and q = 5 then we have a = 39, b = 80; and c = 89 if k = 3 and q = 6 then we have a = 45, b = 108; and c = 117 if k = 3 and q = 7 then we have a = 51, b = 140; and c = 149 if k = 3 and q = 8 then we have a = 57, b = 176; and c = 185 if k = 3 and q = 9 then we have a = 63, b = 216; and c = 225 if k = 3 and q = 10 then we have a = 69, b = 260; and c = 269 if k = 4 and q = 1 then we have a = 24, b = 10; and c = 26 if k = 4 and q = 2 then we have a = 32, b = 24; and c = 40 if k = 4 and q = 3 then we have a = 40, b = 42; and c = 58 if k = 4 and q = 4 then we have a = 48, b = 64; and c = 80 if k = 4 and q = 5 then we have a = 56, b = 90; and c = 106 if k = 4 and q = 6 then we have a = 64, b = 120; and c = 136 if k = 4 and q = 7 then we have a = 72, b = 154; and c = 170 if k = 4 and q = 8 then we have a = 80, b = 192; and c = 208 if k = 4 and q = 9 then we have a = 88, b = 234; and c = 250 if k = 4 and q = 10 then we have a = 96, b = 280; and c = 296 if k = 5 and q = 1 then we have a = 35, b = 12; and c = 37 if k = 5 and q = 2 then we have a = 45, b = 28; and c = 53 if k = 5 and q = 3 then we have a = 55, b = 48; and c = 73 if k = 5 and q = 4 then we have a = 65, b = 72; and c = 97 if k = 5 and q = 5 then we have a = 75, b = 100; and c = 125 if k = 5 and q = 6 then we have a = 85, b = 132; and c = 157 if k = 5 and q = 7 then we have a = 95, b = 168; and c = 193 if k = 5 and q = 8 then we have a = 105, b = 208; and c = 233 if k = 5 and q = 9 then we have a = 115, b = 252; and c = 277 if k = 5 and q = 10 then we have a = 125, b = 300; and c = 325 if k = 6 and q = 1 then we have a = 48, b = 14; and c = 50 if k = 6 and q = 2 then we have a = 60, b = 32; and c = 68 if k = 6 and q = 3 then we have a = 72, b = 54; and c = 90 if k = 6 and q = 4 then we have a = 84, b = 80; and c = 116 if k = 6 and q = 5 then we have a = 96, b = 110; and c = 146 if k = 6 and q = 6 then we have a = 108, b = 144; and c = 180 if k = 6 and q = 7 then we have a = 120, b = 182; and c = 218 if k = 6 and q = 8 then we have a = 132, b = 224; and c = 260 if k = 6 and q = 9 then we have a = 144, b = 270; and c = 306 if k = 6 and q = 10 then we have a = 156, b = 320; and c = 356 if k = 7 and q = 1 then we have a = 63, b = 16; and c = 65 if k = 7 and q = 2 then we have a = 77, b = 36; and c = 85 if k = 7 and q = 3 then we have a = 91, b = 60; and c = 109 if k = 7 and q = 4 then we have a = 105, b = 88; and c = 137 if k = 7 and q = 5 then we have a = 119, b = 120; and c = 169 if k = 7 and q = 6 then we have a = 133, b = 156; and c = 205 if k = 7 and q = 7 then we have a = 147, b = 196; and c = 245 if k = 7 and q = 8 then we have a = 161, b = 240; and c = 289 if k = 7 and q = 9 then we have a = 175, b = 288; and c = 337 if k = 7 and q = 10 then we have a = 189, b = 340; and c = 389 if k = 8 and q = 1 then we have a = 80, b = 18; and c = 82 if k = 8 and q = 2 then we have a = 96, b = 40; and c = 104 if k = 8 and q = 3 then we have a = 112, b = 66; and c = 130 if k = 8 and q = 4 then we have a = 128, b = 96; and c = 160 if k = 8 and q = 5 then we have a = 144, b = 130; and c = 194 if k = 8 and q = 6 then we have a = 160, b = 168; and c = 232 if k = 8 and q = 7 then we have a = 176, b = 210; and c = 274 if k = 8 and q = 8 then we have a = 192, b = 256; and c = 320 if k = 8 and q = 9 then we have a = 208, b = 306; and c = 370 if k = 8 and q = 10 then we have a = 224, b = 360; and c = 424 if k = 9 and q = 1 then we have a = 99, b = 20; and c = 101 if k = 9 and q = 2 then we have a = 117, b = 44; and c = 125 if k = 9 and q = 3 then we have a = 135, b = 72; and c = 153 if k = 9 and q = 4 then we have a = 153, b = 104; and c = 185 if k = 9 and q = 5 then we have a = 171, b = 140; and c = 221 if k = 9 and q = 6 then we have a = 189, b = 180; and c = 261 if k = 9 and q = 7 then we have a = 207, b = 224; and c = 305 if k = 9 and q = 8 then we have a = 225, b = 272; and c = 353 if k = 9 and q = 9 then we have a = 243, b = 324; and c = 405 if k = 9 and q = 10 then we have a = 261, b = 380; and c = 461 if k = 10 and q = 1 then we have a = 120, b = 22; and c = 122 if k = 10 and q = 2 then we have a = 140, b = 48; and c = 148 if k = 10 and q = 3 then we have a = 160, b = 78; and c = 178 if k = 10 and q = 4 then we have a = 180, b = 112; and c = 212 if k = 10 and q = 5 then we have a = 200, b = 150; and c = 250 if k = 10 and q = 6 then we have a = 220, b = 192; and c = 292 if k = 10 and q = 7 then we have a = 240, b = 238; and c = 338 if k = 10 and q = 8 then we have a = 260, b = 288; and c = 388 if k = 10 and q = 9 then we have a = 280, b = 342; and c = 442 if k = 10 and q = 10 then we have a = 300, b = 400; and c = 500 Edwin``` Answer by Alan3354(30993)   (Show Source): You can put this solution on YOUR website!In addition to the extensive list provided by the other tutor, it's interesting that But, there are no instances of integers that fit for any n <> 2 This was recently proven after centuries of effort - Fermat's Last Theorem.