1992.IMO.1数论整除问题与估值反证与不等式放缩。
封包
编辑于 2023年08月27日 01:14

如无必要，勿增实体。

——中世纪经院哲学家 奥卡姆

%7B%5CHuge%20%0A%5Cbegin%7Barray%7D%7Bc%7D%0A(1992.IMO.1)%E8%AF%95%E6%B1%82%E5%87%BA%E6%89%80%E6%9C%89%E7%9A%84%E6%95%B4%E6%95%B0a%2Cb%2Cc%EF%BC%8C%E5%85%B6%E4%B8%AD1%3Ca%3Cb%3Cc%5C%5C%0A%E6%BB%A1%E8%B6%B3%EF%BC%9A(a-1)(b-1)(c-1)%E6%98%AFabc-1%E7%9A%84%E7%BA%A6%E6%95%B0%E3%80%82%5C%5C%0A%5Cend%7Barray%7D%7D%20

%7B%5Clarge%20%0A%5Cbegin%7Barray%7D%7Bc%7D%0A%E8%AE%BE(a-1)%2C(b-1)%2C(c-1)%3Dx%2Cy%2Cz%5C%5C%0A%E2%88%B40%3Cx%3Cy%3Cz%5C%5C%0A%E5%8E%9F%E5%91%BD%E9%A2%98%E5%8D%B3%E8%BD%AC%E5%8C%96%E4%B8%BA%3Axyz%7Cxyz%2Bx%2By%2Bz%2Bxy%2Bxz%2Byz%5C%5C%0A%E5%8D%B3xyz%7Cx%2By%2Bz%2Bxy%2Bxz%2Byz%5C%5C%0A%E2%88%B4x%2By%2Bz%2Bxy%2Bxz%2Byz%E2%89%A5xyz%5C%5C%0A%E6%B3%A8%E6%84%8F%E5%88%B0%E5%B7%A6%E8%BE%B9%E4%BA%8C%E6%AC%A1%E5%BC%8F%EF%BC%8C%E5%8F%B3%E8%BE%B9%E4%B8%89%E6%AC%A1%EF%BC%8C%E6%98%93%E5%AF%BC%E5%87%BA%E7%9F%9B%E7%9B%BE.%5C%5C%0A%E8%8B%A5x%E2%89%A53%2Cy%E2%89%A54%2Cz%E2%89%A55%3A%5C%5C%0A%E5%88%99%5Cfrac%7Bx%2By%2Bz%2Bxy%2Bxz%2Byz%7D%7Bxyz%7D%E2%89%A4%5Cfrac%7B59%7D%7B60%7D%3C1%20%E7%9F%9B%E7%9B%BE%5C%5C%0A%E8%BF%99%E4%B8%AA%E4%BC%B0%E5%80%BC%E5%88%9A%E5%A5%BD%EF%BC%8C%E9%9D%9E%E5%B8%B8%E7%B4%A7%E5%87%91%E3%80%82%5C%5C%0A%E2%88%B4x%E2%89%A42%5C%5C%5C%5C%0A(I)x%3D1%3A%5C%5C%0A%E5%8E%9F%E5%91%BD%E9%A2%98%E8%BD%AC%E5%8C%96%E4%B8%BA%EF%BC%9Ayz%7C2(y%2Bz)%2B1%5C%5C%0A%E6%B3%A8%E6%84%8F%E5%88%B0%E5%B7%A6%E8%BE%B9%E4%B8%BA%E4%B8%80%E6%AC%A1%E5%BC%8F%EF%BC%8C%E5%8F%B3%E8%BE%B9%E4%B8%BA%E4%BA%8C%E6%AC%A1%E5%BC%8F%E6%98%93%E5%AF%BC%E5%87%BA%E7%9F%9B%E7%9B%BE%5C%5C%0A%E8%8B%A5y%E2%89%A55%3A%5C%5C%0A4z%2B1%3E2y%2B2z%2B1%E2%89%A5yz%E2%89%A55z%EF%BC%8C%E7%9F%9B%E7%9B%BE%EF%BC%81%5C%5C%0A%E6%89%80%E4%BB%A5y%E2%89%A44%EF%BC%8C%E5%BE%97%E5%88%B0%E4%BA%86%E4%B8%80%E4%B8%AA%E6%88%91%E4%BB%AC%E8%83%BD%E5%A4%9F%E6%8E%A5%E5%8F%97%E7%9A%84%E8%AE%A1%E7%AE%97%E9%87%8F%E8%8C%83%E5%9B%B4%E3%80%82%5C%5C%0A%E7%BB%8F%E6%A3%80%E9%AA%8Cy%3D3%E6%97%B6%E6%88%90%E7%AB%8B%EF%BC%8C%E6%AD%A4%E6%97%B6z%3D7%E3%80%82%5C%5C%5C%5C%0A(II).%E5%BD%93x%3D2%E6%97%B6%EF%BC%9A%5C%5C%0A3y%2B3z%2B2%E2%89%A5yz%EF%BC%8C%E5%90%8C%E4%B8%8A%E5%8E%9F%E7%90%86%EF%BC%8C%E8%AF%95%E5%9B%BE%E5%AF%BC%E5%87%BA%E7%9F%9B%E7%9B%BE%3A%5C%5C%0A%E8%8B%A5y%E2%89%A57%3A%5C%5C%0A6z%2B2%3E3z%2B3y%2B2%E2%89%A5yz%E2%89%A57z%E7%9F%9B%E7%9B%BE%EF%BC%81%5C%5C%0A%E2%88%B4y%E2%89%A46%EF%BC%8C%E5%BE%97%E5%88%B0%E4%BA%86%E4%B8%80%E4%B8%AA%E6%88%91%E4%BB%AC%E5%8F%AF%E4%BB%A5%E6%8E%A5%E5%8F%97%E7%9A%84%E8%AE%A1%E7%AE%97%E9%87%8F%E8%8C%83%E5%9B%B4%E3%80%82%5C%5C%0A%E7%BB%8F%E6%A3%80%E9%AA%8Cy%3D4%E6%97%B6%E7%AC%A6%E5%90%88%E6%9D%A1%E4%BB%B6%2C%E6%AD%A4%E6%97%B6z%3D14%5C%5C%5C%5C%0A%E7%BB%BC%E4%B8%8A%EF%BC%8C(a%2Cb%2Cc)%3D(2%2C4%2C8)%E6%88%96(3%2C5%2C15)%0A%5Cend%7Barray%7D%7D%20

比较纯粹放缩的数论题，重要的是敢于用反证法放缩条件的尝试，以及通过式子结构来估值的思想，较考验数感。

高中生个人整理，如有错误，欢迎指出。

数学
cv26018128