## 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

Find other solutions

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.