【懸賞50RMB截止8.1日9p.m】修仙題

2023-07-27 20:30 作者:Derivitiva 0人讀過 | 我要投稿

今日份發(fā)瘋////！%……@%（&！#

對于整數(shù) $p%2Cq%2Cr%2Cs$ ，

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記 $A%3D8r%3BB%3D2%5C%20p%5C%20q%5E2%5C%20-%5C%206%5C%20p%5E2%5C%20r%5C%20%2B%5C%2040%5C%20r%5E2-%5C%2050%5C%20q%5C%20s$ ；

$C%3D-2%5C%20q%5E4%2B%5C%2021%5C%20p%5C%20q%5E2r%5C%20-%5C%2040%5C%20p%5E2r%5E2%2B%5C%20160%5C%20r%5E3-%5C%2015%5C%20p%5E2q%5C%20s%5C%20-%5C%20400%5C%20q%5C%20r%5C%20s%5C%20%2B%5C%20125%5C%20p%5C%20s%5E2$ ；

$D%3Dp%5E2q%5E4-%5C%206%5C%20p%5E3q%5E2r%5C%20-%5C%208%5C%20q%5E4r%5C%20%2B%5C%209%5C%20p%5E4r%5E2%2B%5C%2076%5C%20p%5C%20q%5E2r%5E2-%5C%20136%5C%20p%5E2r%5E3$

$%2B%5C%20400%5C%20r%5E4-%5C%2050%5C%20p%5C%20q%5E3s%5C%20%2B%5C%2090%5C%20p%5E2q%5C%20r%5C%20s%5C%20-%5C%201400%5C%20q%5C%20r%5E2s%5C%20%2B%5C%20625%5C%20q%5E2s%5E2%2B%5C%20500%5C%20p%5C%20r%5C%20s%5E2$ ；

$E%3D-2%5C%20p%5C%20q%5E6%2B%5C%2019%5C%20p%5E2q%5E4r%5C%20-%5C%2051%5C%20p%5E3q%5E2r%5E2%2B%5C%203%5C%20q%5E4r%5E2%2B%5C%2032%5C%20p%5E4r%5E3%2B%5C%2076%5C%20p%5C%20q%5E2r%5E3-%5C%20256%5C%20p%5E2r%5E4$

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$-%5C%202400%5C%20q%5C%20r%5E3s%5C%20-%5C%20108%5C%20p%5E5s%5E2-%5C%20325%5C%20p%5E2q%5E2s%5E2%2B%5C%20525%5C%20p%5E3r%5C%20s%5E2%2B%5C%202750%5C%20q%5E2r%5C%20s%5E2-%5C%20500%5C%20p%5C%20r%5E2s%5E2%2B%5C%20625%5C%20p%5C%20q%5C%20s%5E3-%5C%203125%5C%20s%5E4$ ；

$F%3Dq%5E8-%5C%2013%5C%20p%5C%20q%5E6r%5C%20%2B%5C%20p%5E5q%5E2r%5E2%2B%5C%2065%5C%20p%5E2q%5E4r%5E2-%5C%204%5C%20p%5E6r%5E3-%5C%20128%5C%20p%5E3q%5E2r%5E3%2B%5C%2017%5C%20q%5E4r%5E3%2B%5C%2048%5C%20p%5E4r%5E4$

$-%5C%2016%5C%20p%5C%20q%5E2r%5E4-%5C%20192%5C%20p%5E2r%5E5%2B%5C%20256%5C%20r%5E6-%5C%204%5C%20p%5E5q%5E3s%5C%20-%5C%2012%5C%20p%5E2q%5E5s%5C%20%2B%5C%2018%5C%20p%5E6q%5C%20r%5C%20s%5C%20%2B%5C%2012%5C%20p%5E3q%5E3r%5C%20s$

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$-%5C%202000%5C%20p%5C%20r%5E3s%5E2-%5C%201250%5C%20p%5C%20q%5C%20r%5C%20s%5E3%2B%5C%203125%5C%20p%5E2s%5E4-%5C%209375%5C%20r%5C%20s%5E4$ 。

##################################

這四個數(shù) $p%2Cq%2Cr%2Cs$ 擁有以下神奇可愛的性質(zhì)：

（1）存在一個質(zhì)數(shù) $m$ ，同時整除這四個數(shù)，并且 $m%5E2%5Cnmid%20s$

（2）存在一個質(zhì)數(shù) $n$ ，同時整除 $A%2CB%2CC%2CD%2CE%2CF$

（3）這四個數(shù)恰好使關(guān)于x的方程 $x%20%5E5%2Bx%20%5E3p%2Bx%20%5E2q%2Bxr%2Bs%3D0$ 至少有一個根式解

求證： $p%5E2%5Cmid%20F$

在8.1九點(diǎn)前證明者，添加我的微信（主頁有），便可得到我的50元獎賞。當(dāng)然，這題連釣魚題都不是，ABCDEF看起來太扯淡了，但其實不能算太難吧，需要運(yùn)用一篇論文的結(jié)論（我不信有人能自己沒學(xué)過就憑空證明出來），提示一下吧，與一元五次方程有關(guān)。當(dāng)然我并沒有檢驗這仨條件是否矛盾，如能指出矛盾者，同樣可得獎賞！這道題，當(dāng)然假設(shè)不會有矛盾這樣子做就是了。只要您能給出大致的證明，可以直接運(yùn)用論文結(jié)論，方可得到獎賞。另外，只要您和我有共同愛好，就算無法解答、無法推翻我的題目，也可以來和我交流，我急需數(shù)學(xué)朋友（（（

8.1公布答案，同時會提供論文和相關(guān)資料下載鏈接。歡迎各位持續(xù)關(guān)注。

標(biāo)簽：數(shù)學(xué)多項式判別式根式解既約多項式有解條件質(zhì)數(shù)因式分解整除一元五次方程

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