High Quality Content by WIKIPEDIA articles! In mathematics, Legendre's equation is the Diophantine equation ax2 + by2 + cz2 = 0. The equation is named for Adrien Marie Legendre who proved in 1785 that it is solvable in integers x, y, z, not all zero, if and only if ?bc, ?ca and ?ab are quadratic residues modulo a, b and c, respectively, where a, b, c are nonzero, squarefree, pairwise relatively prime integers, not all positive or all negative .

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