Pythagorean triangles – Area + shortest leg is a square

 
 
Find Pythagorean triangles in which the sum of the area and the shortest leg is a square.
 

Here are the first three examples:

 
pt-areaa-1

 

 
 

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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One Response to Pythagorean triangles – Area + shortest leg is a square

  1. Paul says:

    Here is a few more

    {3,4,5,6} , 6 + 3 = 3^2
    {16,30,34,240} , 240 + 16 = 16^2
    {36,48,60,864} , 864 + 36 = 30^2
    {36,160,164,2880} , 2880 + 36 = 54^2
    {64,510,514,16320} , 16320 + 64 = 128^2
    {100,240,260,12000} , 12000 + 100 = 110^2
    {100,1248,1252,62400} , 62400 + 100 = 250^2
    {105,208,233,10920} , 10920 + 105 = 105^2
    {144,2590,2594,186480} , 186480 + 144 = 432^2
    {196,4800,4804,470400} , 470400 + 196 = 686^2
    {216,1450,1466,156600} , 156600 + 216 = 396^2
    {225,1680,1695,189000} , 189000 + 225 = 435^2
    {256,8190,8194,1048320} , 1048320 + 256 = 1024^2
    {289,2448,2465,353736} , 353736 + 289 = 595^2
    {324,13120,13124,2125440} , 2125440 + 324 = 1458^2
    {363,484,605,87846} , 87846 + 363 = 297^2
    {400,19998,20002,3999600} , 3999600 + 400 = 2000^2
    {484,29280,29284,7085760} , 7085760 + 484 = 2662^2
    {576,1680,1776,483840} , 483840 + 576 = 696^2
    {576,41470,41474,11943360} , 11943360 + 576 = 3456^2
    {640,1998,2098,639360} , 639360 + 640 = 800^2
    {672,754,1010,253344} , 253344 + 672 = 504^2
    {676,57120,57124,19306560} , 19306560 + 676 = 4394^2
    {715,1428,1597,510510} , 510510 + 715 = 715^2
    {784,76830,76834,30117360} , 30117360 + 784 = 5488^2
    {900,3696,3804,1663200} , 1663200 + 900 = 1290^2
    {900,101248,101252,45561600} , 45561600 + 900 = 6750^2

    Paul.

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