Make {x^2 + y*z, y^2 + x*z, z^2 + x*y} squares

 
 
Find three distinct positive integers   (x, y, z)   to make the three expressions squares
 

Here are some solutions

x^2+yz 1

 
 
Find other solutions
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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One Response to Make {x^2 + y*z, y^2 + x*z, z^2 + x*y} squares

  1. Paul says:

    Here are a few more, format {x, y, z, a, b, c}. and z <= 500

    13 , 21 , 136 , 55 , 47 , 137
    20 , 48 , 77 , 64 , 62 , 83
    20 , 81 , 404 , 182 , 121 , 406
    21 , 68 , 356 , 157 , 110 , 358
    26 , 42 , 272 , 110 , 94 , 274
    29 , 36 , 260 , 101 , 94 , 262
    33 , 89 , 488 , 211 , 155 , 491
    37 , 69 , 424 , 175 , 143 , 427
    37 , 85 , 312 , 167 , 137 , 317
    39 , 63 , 408 , 165 , 141 , 411
    40 , 96 , 154 , 128 , 124 , 166
    56 , 165 , 221 , 199 , 199 , 241
    60 , 144 , 231 , 192 , 186 , 249
    69 , 80 , 341 , 179 , 173 , 349
    80 , 192 , 308 , 256 , 248 , 332
    100 , 240 , 385 , 320 , 310 , 415
    112 , 330 , 442 , 398 , 398 , 482
    120 , 288 , 462 , 384 , 372 , 498

    Paul.

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