Is there any known complete parametrization of the Diophantine equation $$ A^{2} + B^{2} = C^{2} + D^{2} $$ where $A, B, C, D$ are (positive) rational numbers, or equivalently, integers?
2026-03-28 00:49:27.1774658967
Parametrization of pythagorean-like equation
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Yes, there are. You can put $$A=ms+nt\\B=nt-ms\\C=ms-nt\\D=mt+ns$$ where $m,n,s,t$ are arbitrary.