Find four positive integers to make the three expressions squares

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Find four positive integers to make the three expressions squares

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348^2 + 1015^2 = 353220^2

740^2 + 777^2 = 574980^2

348 X 1015 X 740 X 777 = 450660^2

696^2 + 2030^2 = 1412880^2

1480^2 + 1554^2 = 2299920^2

696 X 2030 X 1480 X 1554 = 1802640^2

1044^2 + 3045^2 = 3178980^2

2220^2 + 2331^2 = 5174820^2

1044 X 3045 X 2220 X 2331 = 4055940^2

435^2 + 3248^2 = 1412880^2

2260^2 + 2373^2 = 5362980^2

435 X 3248 X 2260 X 2373 = 2752680^2

555^2 + 4144^2 = 2299920^2

1356^2 + 3955^2 = 5362980^2

555 X 4144 X 1356 X 3955 = 3512040^2

1392^2 + 4060^2 = 5651520^2

2960^2 + 3108^2 = 9199680^2

1392 X 4060 X 2960 X 3108 = 7210560^2

803^2 + 4380^2 = 3517140^2

2928^2 + 3355^2 = 9823440^2

803 X 4380 X 2928 X 3355 = 5877960^2

1740^2 + 5075^2 = 8830500^2

3700^2 + 3885^2 = 14374500^2

1740 X 5075 X 3700 X 3885 = 11266500^2

245^2 + 6000^2 = 1470000^2

3603^2 + 4804^2 = 17308812^2

245 X 6000 X 3603 X 4804 = 5044200^2

459^2 + 6188^2 = 2840292^2

949^2 + 6132^2 = 5819268^2

459 X 6188 X 949 X 6132 = 4065516^2

2088^2 + 6090^2 = 12715920^2

4440^2 + 4662^2 = 20699280^2

2088 X 6090 X 4440 X 4662 = 16223760^2

870^2 + 6496^2 = 5651520^2

4520^2 + 4746^2 = 21451920^2

870 X 6496 X 4520 X 4746 = 11010720^2

2436^2 + 7105^2 = 17307780^2

5180^2 + 5439^2 = 28174020^2

2436 X 7105 X 5180 X 5439 = 22082340^2

1110^2 + 8288^2 = 9199680^2

2712^2 + 7910^2 = 21451920^2

1110 X 8288 X 2712 X 7910 = 14048160^2

2784^2 + 8120^2 = 22606080^2

5920^2 + 6216^2 = 36798720^2

2784 X 8120 X 5920 X 6216 = 28842240^2

1606^2 + 8760^2 = 14068560^2

5856^2 + 6710^2 = 39293760^2

1606 X 8760 X 5856 X 6710 = 23511840^2

3132^2 + 9135^2 = 28610820^2

6660^2 + 6993^2 = 46573380^2

3132 X 9135 X 6660 X 6993 = 36503460^2

1305^2 + 9744^2 = 12715920^2

6780^2 + 7119^2 = 48266820^2

1305 X 9744 X 6780 X 7119 = 24774120^2

Paul.

What’s your parametric equations?

No parametric solution, I solved for Pythagorean triples for equal hypotenuse, then took all 2 length subsets and tested for m n p q equal to a square.

The first solution is when the hypotenuse is 1073. here my MMa code

Paul.