Legendre's equation

（重定向自Legendre equation）

In mathematics, Legendre's equation is the Diophantine equation

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, square-free, pairwise relatively prime integers, not all positive or all negative .

单词	Legendre equation
释义	Legendre equation 英语百科 Legendre's equation （重定向自Legendre equation） In mathematics, Legendre's equation is the Diophantine equation 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, square-free, pairwise relatively prime integers, not all positive or all negative .
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