Legendre's equation

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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.

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