Question

求不定方程x^2+y^2+z^2=1993的整数解, 详细过程!

Answer 1

{{x -> -43, y -> -12, z -> 0}, {x -> -43, y -> 0,
z -> -12}, {x -> -43, y -> 0, z -> 12}, {x -> -43, y -> 12,
z -> 0}, {x -> -42, y -> -15, z -> -2}, {x -> -42, y -> -15,
z -> 2}, {x -> -42, y -> -2, z -> -15}, {x -> -42, y -> -2,
z -> 15}, {x -> -42, y -> 2, z -> -15}, {x -> -42, y -> 2,
z -> 15}, {x -> -42, y -> 15, z -> -2}, {x -> -42, y -> 15,
z -> 2}, {x -> -38, y -> -18, z -> -15}, {x -> -38, y -> -18,
z -> 15}, {x -> -38, y -> -15, z -> -18}, {x -> -38, y -> -15,
z -> 18}, {x -> -38, y -> 15, z -> -18}, {x -> -38, y -> 15,
z -> 18}, {x -> -38, y -> 18, z -> -15}, {x -> -38, y -> 18,
z -> 15}, {x -> -36, y -> -24, z -> -11}, {x -> -36, y -> -24,
z -> 11}, {x -> -36, y -> -21, z -> -16}, {x -> -36, y -> -21,
z -> 16}, {x -> -36, y -> -16, z -> -21}, {x -> -36, y -> -16,
z -> 21}, {x -> -36, y -> -11, z -> -24}, {x -> -36, y -> -11,
z -> 24}, {x -> -36, y -> 11, z -> -24}, {x -> -36, y -> 11,
z -> 24}, {x -> -36, y -> 16, z -> -21}, {x -> -36, y -> 16,
z -> 21}, {x -> -36, y -> 21, z -> -16}, {x -> -36, y -> 21,
z -> 16}, {x -> -36, y -> 24, z -> -11}, {x -> -36, y -> 24,
z -> 11}, {x -> -33, y -> -30, z -> -2}, {x -> -33, y -> -30,
z -> 2}, {x -> -33, y -> -2, z -> -30}, {x -> -33, y -> -2,
z -> 30}, {x -> -33, y -> 2, z -> -30}, {x -> -33, y -> 2,
z -> 30}, {x -> -33, y -> 30, z -> -2}, {x -> -33, y -> 30,
z -> 2}, {x -> -30, y -> -33, z -> -2}, {x -> -30, y -> -33,
z -> 2}, {x -> -30, y -> -2, z -> -33}, {x -> -30, y -> -2,
z -> 33}, {x -> -30, y -> 2, z -> -33}, {x -> -30, y -> 2,
z -> 33}, {x -> -30, y -> 33, z -> -2}, {x -> -30, y -> 33,
z -> 2}, {x -> -29, y -> -24, z -> -24}, {x -> -29, y -> -24,
z -> 24}, {x -> -29, y -> 24, z -> -24}, {x -> -29, y -> 24,
z -> 24}, {x -> -24, y -> -36, z -> -11}, {x -> -24, y -> -36,
z -> 11}, {x -> -24, y -> -29, z -> -24}, {x -> -24, y -> -29,
z -> 24}, {x -> -24, y -> -24, z -> -29}, {x -> -24, y -> -24,
z -> 29}, {x -> -24, y -> -11, z -> -36}, {x -> -24, y -> -11,
z -> 36}, {x -> -24, y -> 11, z -> -36}, {x -> -24, y -> 11,
z -> 36}, {x -> -24, y -> 24, z -> -29}, {x -> -24, y -> 24,
z -> 29}, {x -> -24, y -> 29, z -> -24}, {x -> -24, y -> 29,
z -> 24}, {x -> -24, y -> 36, z -> -11}, {x -> -24, y -> 36,
z -> 11}, {x -> -21, y -> -36, z -> -16}, {x -> -21, y -> -36,
z -> 16}, {x -> -21, y -> -16, z -> -36}, {x -> -21, y -> -16,
z -> 36}, {x -> -21, y -> 16, z -> -36}, {x -> -21, y -> 16,
z -> 36}, {x -> -21, y -> 36, z -> -16}, {x -> -21, y -> 36,
z -> 16}, {x -> -18, y -> -38, z -> -15}, {x -> -18, y -> -38,
z -> 15}, {x -> -18, y -> -15, z -> -38}, {x -> -18, y -> -15,
z -> 38}, {x -> -18, y -> 15, z -> -38}, {x -> -18, y -> 15,
z -> 38}, {x -> -18, y -> 38, z -> -15}, {x -> -18, y -> 38,
z -> 15}, {x -> -16, y -> -36, z -> -21}, {x -> -16, y -> -36,
z -> 21}, {x -> -16, y -> -21, z -> -36}, {x -> -16, y -> -21,
z -> 36}, {x -> -16, y -> 21, z -> -36}, {x -> -16, y -> 21,
z -> 36}, {x -> -16, y -> 36, z -> -21}, {x -> -16, y -> 36,
z -> 21}, {x -> -15, y -> -42, z -> -2}, {x -> -15, y -> -42,
z -> 2}, {x -> -15, y -> -38, z -> -18}, {x -> -15, y -> -38,
z -> 18}, {x -> -15, y -> -18, z -> -38}, {x -> -15, y -> -18,
z -> 38}, {x -> -15, y -> -2, z -> -42}, {x -> -15, y -> -2,
z -> 42}, {x -> -15, y -> 2, z -> -42}, {x -> -15, y -> 2,
z -> 42}, {x -> -15, y -> 18, z -> -38}, {x -> -15, y -> 18,
z -> 38}, {x -> -15, y -> 38, z -> -18}, {x -> -15, y -> 38,
z -> 18}, {x -> -15, y -> 42, z -> -2}, {x -> -15, y -> 42,
z -> 2}, {x -> -12, y -> -43, z -> 0}, {x -> -12, y -> 0,
z -> -43}, {x -> -12, y -> 0, z -> 43}, {x -> -12, y -> 43,
z -> 0}, {x -> -11, y -> -36, z -> -24}, {x -> -11, y -> -36,
z -> 24}, {x -> -11, y -> -24, z -> -36}, {x -> -11, y -> -24,
z -> 36}, {x -> -11, y -> 24, z -> -36}, {x -> -11, y -> 24,
z -> 36}, {x -> -11, y -> 36, z -> -24}, {x -> -11, y -> 36,
z -> 24}, {x -> -2, y -> -42, z -> -15}, {x -> -2, y -> -42,
z -> 15}, {x -> -2, y -> -33, z -> -30}, {x -> -2, y -> -33,
z -> 30}, {x -> -2, y -> -30, z -> -33}, {x -> -2, y -> -30,
z -> 33}, {x -> -2, y -> -15, z -> -42}, {x -> -2, y -> -15,
z -> 42}, {x -> -2, y -> 15, z -> -42}, {x -> -2, y -> 15,
z -> 42}, {x -> -2, y -> 30, z -> -33}, {x -> -2, y -> 30,
z -> 33}, {x -> -2, y -> 33, z -> -30}, {x -> -2, y -> 33,
z -> 30}, {x -> -2, y -> 42, z -> -15}, {x -> -2, y -> 42,
z -> 15}, {x -> 0, y -> -43, z -> -12}, {x -> 0, y -> -43,
z -> 12}, {x -> 0, y -> -12, z -> -43}, {x -> 0, y -> -12,
z -> 43}, {x -> 0, y -> 12, z -> -43}, {x -> 0, y -> 12,
z -> 43}, {x -> 0, y -> 43, z -> -12}, {x -> 0, y -> 43,
z -> 12}, {x -> 2, y -> -42, z -> -15}, {x -> 2, y -> -42,
z -> 15}, {x -> 2, y -> -33, z -> -30}, {x -> 2, y -> -33,
z -> 30}, {x -> 2, y -> -30, z -> -33}, {x -> 2, y -> -30,
z -> 33}, {x -> 2, y -> -15, z -> -42}, {x -> 2, y -> -15,
z -> 42}, {x -> 2, y -> 15, z -> -42}, {x -> 2, y -> 15,
z -> 42}, {x -> 2, y -> 30, z -> -33}, {x -> 2, y -> 30,
z -> 33}, {x -> 2, y -> 33, z -> -30}, {x -> 2, y -> 33,
z -> 30}, {x -> 2, y -> 42, z -> -15}, {x -> 2, y -> 42,
z -> 15}, {x -> 11, y -> -36, z -> -24}, {x -> 11, y -> -36,
z -> 24}, {x -> 11, y -> -24, z -> -36}, {x -> 11, y -> -24,
z -> 36}, {x -> 11, y -> 24, z -> -36}, {x -> 11, y -> 24,
z -> 36}, {x -> 11, y -> 36, z -> -24}, {x -> 11, y -> 36,
z -> 24}, {x -> 12, y -> -43, z -> 0}, {x -> 12, y -> 0,
z -> -43}, {x -> 12, y -> 0, z -> 43}, {x -> 12, y -> 43,
z -> 0}, {x -> 15, y -> -42, z -> -2}, {x -> 15, y -> -42,
z -> 2}, {x -> 15, y -> -38, z -> -18}, {x -> 15, y -> -38,
z -> 18}, {x -> 15, y -> -18, z -> -38}, {x -> 15, y -> -18,
z -> 38}, {x -> 15, y -> -2, z -> -42}, {x -> 15, y -> -2,
z -> 42}, {x -> 15, y -> 2, z -> -42}, {x -> 15, y -> 2,
z -> 42}, {x -> 15, y -> 18, z -> -38}, {x -> 15, y -> 18,
z -> 38}, {x -> 15, y -> 38, z -> -18}, {x -> 15, y -> 38,
z -> 18}, {x -> 15, y -> 42, z -> -2}, {x -> 15, y -> 42,
z -> 2}, {x -> 16, y -> -36, z -> -21}, {x -> 16, y -> -36,
z -> 21}, {x -> 16, y -> -21, z -> -36}, {x -> 16, y -> -21,
z -> 36}, {x -> 16, y -> 21, z -> -36}, {x -> 16, y -> 21,
z -> 36}, {x -> 16, y -> 36, z -> -21}, {x -> 16, y -> 36,
z -> 21}, {x -> 18, y -> -38, z -> -15}, {x -> 18, y -> -38,
z -> 15}, {x -> 18, y -> -15, z -> -38}, {x -> 18, y -> -15,
z -> 38}, {x -> 18, y -> 15, z -> -38}, {x -> 18, y -> 15,
z -> 38}, {x -> 18, y -> 38, z -> -15}, {x -> 18, y -> 38,
z -> 15}, {x -> 21, y -> -36, z -> -16}, {x -> 21, y -> -36,
z -> 16}, {x -> 21, y -> -16, z -> -36}, {x -> 21, y -> -16,
z -> 36}, {x -> 21, y -> 16, z -> -36}, {x -> 21, y -> 16,
z -> 36}, {x -> 21, y -> 36, z -> -16}, {x -> 21, y -> 36,
z -> 16}, {x -> 24, y -> -36, z -> -11}, {x -> 24, y -> -36,
z -> 11}, {x -> 24, y -> -29, z -> -24}, {x -> 24, y -> -29,
z -> 24}, {x -> 24, y -> -24, z -> -29}, {x -> 24, y -> -24,
z -> 29}, {x -> 24, y -> -11, z -> -36}, {x -> 24, y -> -11,
z -> 36}, {x -> 24, y -> 11, z -> -36}, {x -> 24, y -> 11,
z -> 36}, {x -> 24, y -> 24, z -> -29}, {x -> 24, y -> 24,
z -> 29}, {x -> 24, y -> 29, z -> -24}, {x -> 24, y -> 29,
z -> 24}, {x -> 24, y -> 36, z -> -11}, {x -> 24, y -> 36,
z -> 11}, {x -> 29, y -> -24, z -> -24}, {x -> 29, y -> -24,
z -> 24}, {x -> 29, y -> 24, z -> -24}, {x -> 29, y -> 24,
z -> 24}, {x -> 30, y -> -33, z -> -2}, {x -> 30, y -> -33,
z -> 2}, {x -> 30, y -> -2, z -> -33}, {x -> 30, y -> -2,
z -> 33}, {x -> 30, y -> 2, z -> -33}, {x -> 30, y -> 2,
z -> 33}, {x -> 30, y -> 33, z -> -2}, {x -> 30, y -> 33,
z -> 2}, {x -> 33, y -> -30, z -> -2}, {x -> 33, y -> -30,
z -> 2}, {x -> 33, y -> -2, z -> -30}, {x -> 33, y -> -2,
z -> 30}, {x -> 33, y -> 2, z -> -30}, {x -> 33, y -> 2,
z -> 30}, {x -> 33, y -> 30, z -> -2}, {x -> 33, y -> 30,
z -> 2}, {x -> 36, y -> -24, z -> -11}, {x -> 36, y -> -24,
z -> 11}, {x -> 36, y -> -21, z -> -16}, {x -> 36, y -> -21,
z -> 16}, {x -> 36, y -> -16, z -> -21}, {x -> 36, y -> -16,
z -> 21}, {x -> 36, y -> -11, z -> -24}, {x -> 36, y -> -11,
z -> 24}, {x -> 36, y -> 11, z -> -24}, {x -> 36, y -> 11,
z -> 24}, {x -> 36, y -> 16, z -> -21}, {x -> 36, y -> 16,
z -> 21}, {x -> 36, y -> 21, z -> -16}, {x -> 36, y -> 21,
z -> 16}, {x -> 36, y -> 24, z -> -11}, {x -> 36, y -> 24,
z -> 11}, {x -> 38, y -> -18, z -> -15}, {x -> 38, y -> -18,
z -> 15}, {x -> 38, y -> -15, z -> -18}, {x -> 38, y -> -15,
z -> 18}, {x -> 38, y -> 15, z -> -18}, {x -> 38, y -> 15, z -> 18},
{x -> 38, y -> 18, z -> -15}, {x -> 38, y -> 18, z -> 15}, {x -> 42,
y -> -15, z -> -2}, {x -> 42, y -> -15, z -> 2}, {x -> 42, y -> -2,
z -> -15}, {x -> 42, y -> -2, z -> 15}, {x -> 42, y -> 2,
z -> -15}, {x -> 42, y -> 2, z -> 15}, {x -> 42, y -> 15,
z -> -2}, {x -> 42, y -> 15, z -> 2}, {x -> 43, y -> -12,
z -> 0}, {x -> 43, y -> 0, z -> -12}, {x -> 43, y -> 0,
z -> 12}, {x -> 43, y -> 12, z -> 0}}

追问

怎么来的?

追答

不定方程的解：要不用软件，要不使用参数方程。

追问

这说明你没有弄清我的意思,我说过我需要的是解题过程,更多的是思路,不是结果.更不是计算机程序的结果! 计算机结果, 我也能做,验证性的讨论对数论而言是非常差的!

追答

这个是数论的问题，写出来比答案还复杂。建议下载这本书---数论导引（华罗庚）

追问

我的问题还是没有解决，不过感谢你的热心回答！