document.write( "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.
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Algebra.Com's Answer #200676 by Edwin McCravy(20055)\"\" \"About 
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.
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document.write( "One formula is\r\n" );
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document.write( "\"system%28a+=+k%28k%2B2q%29%2Cb+=+2q%28k%2Bq%29%2Cc+=+k%5E2%2B2qk%2B2q%5E2%29\"\r\n" );
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document.write( "where you can substitute any positive integers for \"q\" and \"k\".\r\n" );
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document.write( "if k = 1 and q = 1 then we have a = 3, b = 4; and c = 5\r\n" );
document.write( "if k = 1 and q = 2 then we have a = 5, b = 12; and c = 13\r\n" );
document.write( "if k = 1 and q = 3 then we have a = 7, b = 24; and c = 25\r\n" );
document.write( "if k = 1 and q = 4 then we have a = 9, b = 40; and c = 41\r\n" );
document.write( "if k = 1 and q = 5 then we have a = 11, b = 60; and c = 61\r\n" );
document.write( "if k = 1 and q = 6 then we have a = 13, b = 84; and c = 85\r\n" );
document.write( "if k = 1 and q = 7 then we have a = 15, b = 112; and c = 113\r\n" );
document.write( "if k = 1 and q = 8 then we have a = 17, b = 144; and c = 145\r\n" );
document.write( "if k = 1 and q = 9 then we have a = 19, b = 180; and c = 181\r\n" );
document.write( "if k = 1 and q = 10 then we have a = 21, b = 220; and c = 221\r\n" );
document.write( "if k = 2 and q = 1 then we have a = 8, b = 6; and c = 10\r\n" );
document.write( "if k = 2 and q = 2 then we have a = 12, b = 16; and c = 20\r\n" );
document.write( "if k = 2 and q = 3 then we have a = 16, b = 30; and c = 34\r\n" );
document.write( "if k = 2 and q = 4 then we have a = 20, b = 48; and c = 52\r\n" );
document.write( "if k = 2 and q = 5 then we have a = 24, b = 70; and c = 74\r\n" );
document.write( "if k = 2 and q = 6 then we have a = 28, b = 96; and c = 100\r\n" );
document.write( "if k = 2 and q = 7 then we have a = 32, b = 126; and c = 130\r\n" );
document.write( "if k = 2 and q = 8 then we have a = 36, b = 160; and c = 164\r\n" );
document.write( "if k = 2 and q = 9 then we have a = 40, b = 198; and c = 202\r\n" );
document.write( "if k = 2 and q = 10 then we have a = 44, b = 240; and c = 244\r\n" );
document.write( "if k = 3 and q = 1 then we have a = 15, b = 8; and c = 17\r\n" );
document.write( "if k = 3 and q = 2 then we have a = 21, b = 20; and c = 29\r\n" );
document.write( "if k = 3 and q = 3 then we have a = 27, b = 36; and c = 45\r\n" );
document.write( "if k = 3 and q = 4 then we have a = 33, b = 56; and c = 65\r\n" );
document.write( "if k = 3 and q = 5 then we have a = 39, b = 80; and c = 89\r\n" );
document.write( "if k = 3 and q = 6 then we have a = 45, b = 108; and c = 117\r\n" );
document.write( "if k = 3 and q = 7 then we have a = 51, b = 140; and c = 149\r\n" );
document.write( "if k = 3 and q = 8 then we have a = 57, b = 176; and c = 185\r\n" );
document.write( "if k = 3 and q = 9 then we have a = 63, b = 216; and c = 225\r\n" );
document.write( "if k = 3 and q = 10 then we have a = 69, b = 260; and c = 269\r\n" );
document.write( "if k = 4 and q = 1 then we have a = 24, b = 10; and c = 26\r\n" );
document.write( "if k = 4 and q = 2 then we have a = 32, b = 24; and c = 40\r\n" );
document.write( "if k = 4 and q = 3 then we have a = 40, b = 42; and c = 58\r\n" );
document.write( "if k = 4 and q = 4 then we have a = 48, b = 64; and c = 80\r\n" );
document.write( "if k = 4 and q = 5 then we have a = 56, b = 90; and c = 106\r\n" );
document.write( "if k = 4 and q = 6 then we have a = 64, b = 120; and c = 136\r\n" );
document.write( "if k = 4 and q = 7 then we have a = 72, b = 154; and c = 170\r\n" );
document.write( "if k = 4 and q = 8 then we have a = 80, b = 192; and c = 208\r\n" );
document.write( "if k = 4 and q = 9 then we have a = 88, b = 234; and c = 250\r\n" );
document.write( "if k = 4 and q = 10 then we have a = 96, b = 280; and c = 296\r\n" );
document.write( "if k = 5 and q = 1 then we have a = 35, b = 12; and c = 37\r\n" );
document.write( "if k = 5 and q = 2 then we have a = 45, b = 28; and c = 53\r\n" );
document.write( "if k = 5 and q = 3 then we have a = 55, b = 48; and c = 73\r\n" );
document.write( "if k = 5 and q = 4 then we have a = 65, b = 72; and c = 97\r\n" );
document.write( "if k = 5 and q = 5 then we have a = 75, b = 100; and c = 125\r\n" );
document.write( "if k = 5 and q = 6 then we have a = 85, b = 132; and c = 157\r\n" );
document.write( "if k = 5 and q = 7 then we have a = 95, b = 168; and c = 193\r\n" );
document.write( "if k = 5 and q = 8 then we have a = 105, b = 208; and c = 233\r\n" );
document.write( "if k = 5 and q = 9 then we have a = 115, b = 252; and c = 277\r\n" );
document.write( "if k = 5 and q = 10 then we have a = 125, b = 300; and c = 325\r\n" );
document.write( "if k = 6 and q = 1 then we have a = 48, b = 14; and c = 50\r\n" );
document.write( "if k = 6 and q = 2 then we have a = 60, b = 32; and c = 68\r\n" );
document.write( "if k = 6 and q = 3 then we have a = 72, b = 54; and c = 90\r\n" );
document.write( "if k = 6 and q = 4 then we have a = 84, b = 80; and c = 116\r\n" );
document.write( "if k = 6 and q = 5 then we have a = 96, b = 110; and c = 146\r\n" );
document.write( "if k = 6 and q = 6 then we have a = 108, b = 144; and c = 180\r\n" );
document.write( "if k = 6 and q = 7 then we have a = 120, b = 182; and c = 218\r\n" );
document.write( "if k = 6 and q = 8 then we have a = 132, b = 224; and c = 260\r\n" );
document.write( "if k = 6 and q = 9 then we have a = 144, b = 270; and c = 306\r\n" );
document.write( "if k = 6 and q = 10 then we have a = 156, b = 320; and c = 356\r\n" );
document.write( "if k = 7 and q = 1 then we have a = 63, b = 16; and c = 65\r\n" );
document.write( "if k = 7 and q = 2 then we have a = 77, b = 36; and c = 85\r\n" );
document.write( "if k = 7 and q = 3 then we have a = 91, b = 60; and c = 109\r\n" );
document.write( "if k = 7 and q = 4 then we have a = 105, b = 88; and c = 137\r\n" );
document.write( "if k = 7 and q = 5 then we have a = 119, b = 120; and c = 169\r\n" );
document.write( "if k = 7 and q = 6 then we have a = 133, b = 156; and c = 205\r\n" );
document.write( "if k = 7 and q = 7 then we have a = 147, b = 196; and c = 245\r\n" );
document.write( "if k = 7 and q = 8 then we have a = 161, b = 240; and c = 289\r\n" );
document.write( "if k = 7 and q = 9 then we have a = 175, b = 288; and c = 337\r\n" );
document.write( "if k = 7 and q = 10 then we have a = 189, b = 340; and c = 389\r\n" );
document.write( "if k = 8 and q = 1 then we have a = 80, b = 18; and c = 82\r\n" );
document.write( "if k = 8 and q = 2 then we have a = 96, b = 40; and c = 104\r\n" );
document.write( "if k = 8 and q = 3 then we have a = 112, b = 66; and c = 130\r\n" );
document.write( "if k = 8 and q = 4 then we have a = 128, b = 96; and c = 160\r\n" );
document.write( "if k = 8 and q = 5 then we have a = 144, b = 130; and c = 194\r\n" );
document.write( "if k = 8 and q = 6 then we have a = 160, b = 168; and c = 232\r\n" );
document.write( "if k = 8 and q = 7 then we have a = 176, b = 210; and c = 274\r\n" );
document.write( "if k = 8 and q = 8 then we have a = 192, b = 256; and c = 320\r\n" );
document.write( "if k = 8 and q = 9 then we have a = 208, b = 306; and c = 370\r\n" );
document.write( "if k = 8 and q = 10 then we have a = 224, b = 360; and c = 424\r\n" );
document.write( "if k = 9 and q = 1 then we have a = 99, b = 20; and c = 101\r\n" );
document.write( "if k = 9 and q = 2 then we have a = 117, b = 44; and c = 125\r\n" );
document.write( "if k = 9 and q = 3 then we have a = 135, b = 72; and c = 153\r\n" );
document.write( "if k = 9 and q = 4 then we have a = 153, b = 104; and c = 185\r\n" );
document.write( "if k = 9 and q = 5 then we have a = 171, b = 140; and c = 221\r\n" );
document.write( "if k = 9 and q = 6 then we have a = 189, b = 180; and c = 261\r\n" );
document.write( "if k = 9 and q = 7 then we have a = 207, b = 224; and c = 305\r\n" );
document.write( "if k = 9 and q = 8 then we have a = 225, b = 272; and c = 353\r\n" );
document.write( "if k = 9 and q = 9 then we have a = 243, b = 324; and c = 405\r\n" );
document.write( "if k = 9 and q = 10 then we have a = 261, b = 380; and c = 461\r\n" );
document.write( "if k = 10 and q = 1 then we have a = 120, b = 22; and c = 122\r\n" );
document.write( "if k = 10 and q = 2 then we have a = 140, b = 48; and c = 148\r\n" );
document.write( "if k = 10 and q = 3 then we have a = 160, b = 78; and c = 178\r\n" );
document.write( "if k = 10 and q = 4 then we have a = 180, b = 112; and c = 212\r\n" );
document.write( "if k = 10 and q = 5 then we have a = 200, b = 150; and c = 250\r\n" );
document.write( "if k = 10 and q = 6 then we have a = 220, b = 192; and c = 292\r\n" );
document.write( "if k = 10 and q = 7 then we have a = 240, b = 238; and c = 338\r\n" );
document.write( "if k = 10 and q = 8 then we have a = 260, b = 288; and c = 388\r\n" );
document.write( "if k = 10 and q = 9 then we have a = 280, b = 342; and c = 442\r\n" );
document.write( "if k = 10 and q = 10 then we have a = 300, b = 400; and c = 500\r\n" );
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document.write( "Edwin
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