散文網(wǎng) » 科技 »學(xué)習(xí) » 2007.IMO.5數(shù)論——無窮遞降法，與對稱性證明技巧。

2007.IMO.5數(shù)論——無窮遞降法，與對稱性證明技巧。

2023-08-27 20:31 作者:封包 0人讀過 | 我要投稿

不要向你的欲望讓步。

——雅克拉康

$%7B%5CHuge%20%0A%5Cbegin%7Barray%7D%7Bc%7D%0A(2007.IMO.6)a%2Cb%5Cin%20%5Cmathbb%7BN%5E%2B%7D%2C4ab%7C(4a%5E2-1)%5E2%5C%5C%0A%E8%AF%81%E6%98%8E%3Aa%3Db%20%0A%5Cend%7Barray%7D%7D%20$

$%7B%5Clarge%20%0A%5Cbegin%7Barray%7D%7Bc%7D%0A%E7%94%B1%E9%A2%98%E7%9B%AE%E5%B7%B2%E7%9F%A5%3A1%5Cequiv%201%5E2%5Cequiv%20(4ab)%5E2%5Cmod%7B4ab-1%7D%5C%5C%0A%E2%88%B4(4b%5E2-1)%5E2%5Cequiv%20(4b%5E2-(4ab)%5E2)%5E2%5C%5C%5Cequiv%2016b%5E4(4a%5E2-1)%5Cequiv%200%20%5Cmod%7B4ab-1%7D%5C%5C%0A%E2%88%B44ab-1%7C(4b%5E2-1)%5E2%E6%88%91%E4%BB%AC%E5%BE%97%E5%88%B0%E4%BA%86%E5%AF%B9%E7%A7%B0%E6%80%A7%5C%5C%5C%5C%0A%E4%B8%8B%E9%9D%A2%E8%80%83%E8%99%91%E6%97%A0%E7%A9%B7%E9%80%92%E9%99%8D%E6%B3%95%E5%8F%8D%E8%AF%81%E6%8E%A8%E5%87%BA%E7%9F%9B%E7%9B%BE%EF%BC%9A%5C%5C%0A%E5%BD%93a%3Cb%0A%E5%85%88%E8%80%83%E8%99%91%E8%AE%BE%5Cfrac%7B(4a%5E2-1)%5E2%7D%7B4ab-1%7D%3DS%E7%9A%84%E8%A7%A3(a%2Cb)%5C%5C%0A%E6%BB%A1%E8%B6%B3%E4%B8%8D%E5%AE%9A%E6%96%B9%E7%A8%8B%E7%9A%84%E6%9C%80%E5%B0%8F%E8%A7%A3(a%2Bb)%E6%9C%80%E5%B0%8F%E3%80%82%5C%5C%0A%E5%88%99S(4ab-1)%5Cequiv%20(4a%5E2-1)%5E2%20%5Cmod%7B4a%7D%5C%5C%0A4ab%5Cequiv%200%2C4a%5E2%5Cequiv%200%20%5Cmod%7B4a%7D%5C%5C%0A%E6%89%80%E4%BB%A5S%5Cequiv%20-1%20%5Cmod%7B4a%7D%5C%5C%0A%E8%AE%BES%3D4ac-1%5C%5C%0A%E9%82%A3%E4%B9%884ac-1%3DS%EF%BC%9C4a%5E2-1%5C%5C%0A%E2%88%B4c%3Ca%3Cb%5C%5C%0A(4ac-1)(4ab-1)%3D(4a%5E2-1)%5E2%5C%5C%0A%E9%82%A3%E4%B9%88(a%2Cc)%E6%98%AF%E6%AF%94(a%2Cb)%E6%9B%B4%E5%B0%8F%E7%9A%84%E4%B8%80%E7%BB%84%E8%A7%A3%EF%BC%8C%E7%9F%9B%E7%9B%BE%EF%BC%81%5C%5C%5C%5C%0A%E5%BD%93a%3Eb%E6%97%B6%EF%BC%9A%E7%94%B14ab-1%7C(4b%5E2-1)%5E2%E5%AF%B9%E7%A7%B0%E6%80%A7%E5%90%8C%E7%90%86%E5%BE%97%E5%88%B0%E7%9F%9B%E7%9B%BE%5C%5C%5C%5C%0A%E6%95%85a%3Db%5C%5C%0A%E8%AF%81%E6%AF%95%E3%80%82%0A%5Cend%7Barray%7D%7D%20$