• 2022-06-18
    试证: 对任意的复数[tex=0.5x0.786]C7x+w8+jOPZzxFrGGne6Dw==[/tex]及整数 [tex=0.929x0.786]VF0GLe2VBE/4VKNzpyOfFg==[/tex],[tex=4.643x1.357]WaKgiVQnt6FFP5so8Y7FJ77P2vR+QerbEuMpohzpfQguZbmKJxqkaM8kMyOxMm/DI+40NEZ0sR8PEaUwcn51WA==[/tex]
  • 证明:分别就 [tex=0.929x0.786]VF0GLe2VBE/4VKNzpyOfFg==[/tex]为正整数,零,负整数的情形证明,仅以正整数为例. (数学归纳法)当 [tex=2.214x1.0]/SshMuJUYJhx8e443Hww5Q==[/tex]时,等式显然成立. 假设 [tex=3.5x1.143]Gx4Txzhj1TagF4+QMFcWbA==[/tex] 时成立, 即有 [tex=6.714x1.571]2WFXeptbGgkc8eUXQzh7gJNPu6jnhDC9PQW2X7sRMrIeRBq+ICHiIG6xO+KirfxnsCEBad15mETfOKaxTH792A==[/tex]那么当[tex=2.214x1.0]J8sHjXanufngceD6/vvfdw==[/tex] 时,[tex=14.5x1.643]xJDiZFs5E8iWahOGpkQoRRr3c4aVmijQopisQvUje6iWwwe2jl3xwz+KxF+ayrrN6IOUlA94aQj+MgBqYzOh4whO/7huXdW0BPLkY9nzrSy0OP+r47W+PaerRwKM0O+sxBY+bRpwvFjwopPOJSKDFVDpHt221kMftW0sjvrimEpDxibF8GS5AiNF9270sn2kneOvb4hxX2c2C9YclzXy6w==[/tex]则等式成立. 故 [tex=9.929x1.5]2WFXeptbGgkc8eUXQzh7gD4w/I52qqSqzL9SKxmlw02IZ4tjwtTmySbsBVoKI4ryD5tMJXMrTvtTK2LG6zVtgX7kpPHN5Aphr+xqyY9mj2KNF404mIA8/HzwXrRXkX/e[/tex]

    内容

    • 0

       设 [tex=0.929x0.786]VF0GLe2VBE/4VKNzpyOfFg==[/tex] 是形如[tex=2.429x1.143]fdxby+wIXypZqWS2dpwUkA==[/tex] 的整数,试证: 不定方程[tex=6.0x1.429]OuwRYs6qkoGwOGzBs+NLYpKGlHnqo6fVqLQAVOIv/+E=[/tex] 没有整数解.

    • 1

      设[tex=0.929x0.786]VF0GLe2VBE/4VKNzpyOfFg==[/tex] 是形如[tex=2.429x1.143]Eki7zUebwWHx8Qv6OvC0lg==[/tex] 的整数,试证: 不定方程 [tex=6.0x1.429]JfMnpkdfUBckNje06oWbk8fefrS8Z/gIZJbcH91q9YI=[/tex]没有整数解.

    • 2

      [br][/br]设 [tex=0.929x0.786]VF0GLe2VBE/4VKNzpyOfFg==[/tex] 是大于 1 的整数,证明不大于 [tex=0.929x0.786]VF0GLe2VBE/4VKNzpyOfFg==[/tex] 且与 [tex=0.929x0.786]VF0GLe2VBE/4VKNzpyOfFg==[/tex] 互素的所有正整数之和为 [tex=4.357x2.357]sjK4NrbKWB0OUoVSqml3orVuMxOKsDVzHVIS7pFHk1g=[/tex]

    • 3

      >>>x= [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9]>>>print(x.sort()) 语句运行结果正确的是( )。 A: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] B: [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9] C: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0] D: ['2', '4', '0', '6', '10', '7', '8', '3', '9', '1', '5']

    • 4

      判断下列命题是否为真:(1)[tex=3.643x1.357]/5abqJjwKZ1qr+6hsVFF5EBvfq3ggOFNlHMClz0h9nk=[/tex](2)[tex=2.929x1.357]rGJpyjIjJpbcoBTWxP0Jiw==[/tex](3)[tex=4.5x1.357]2wycHMoqU83MyEp17iBils58bR7YLuCTI2G9NVAdlfY=[/tex](4)[tex=5.214x1.357]CTz2gu+IIm1GgNmYMGaduCRtA41wnW4WqwRWwEhq6aA=[/tex](5)[tex=4.857x1.357]1DcE2BMMOaZhTuxR/mjgsboXxfg5ET59Dp4I/jjEDuw=[/tex](6)[tex=4.643x1.357]BSryrsQYOvTP2hTWRu6t4nAuJwlSs4L9jaq70EpB+Us=[/tex](7)若[tex=6.0x1.357]y0IZLUnBO88nR8WBZYvd7QXv5S1OMINV5cQNzPyiyAc=[/tex],则[tex=3.429x1.357]1brfPwTkVVIX4GfoMIUskA==[/tex](8)若[tex=7.643x1.357]MhLfJXZnhbXiB0x3oNtFzThV4Y1mJxe1VYr7PkJE/T6hmTD3WWp+UxbNwvUQ6DHk[/tex],则[tex=4.143x1.357]LZUA94ISo1po5HWsOVeBCjo0rMvj7uw3bGw5HiZenrI=[/tex]