Let a, b, c be nonzero integers having no prime factors ≡ 3 (mod 4), not all of the same sign, abc squarefree, and for which Legendre's equation ax2 + by2 + cz2 = 0 is solvable in nonzero integers x, y, z. A property is proved yielding a congruence which must be satisfied by any solution x, y, z.

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Persistent URL dx.doi.org/10.1016/0022-314X(83)90035-5
Journal Journal of Number Theory
Hudson, R.H. (Richard H.), & Williams, K.S. (1983). On Legendre's equation ax2 + by2 + cz2 = 0. Journal of Number Theory, 16(1), 100–105. doi:10.1016/0022-314X(83)90035-5