【悬赏50RMB截止8.1日9p.m】修仙题

2023-07-27 20:30 作者:Derivitiva 0人读过 | 我要投稿

今日份发疯////！%……@%（&！#

对于整数 $p%2Cq%2Cr%2Cs$ ，

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

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

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

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

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

$%2B%5C%20512%5C%20r%5E5-%5C%2031%5C%20p%5E3q%5E3s%5C%20-%5C%2058%5C%20q%5E5s%5C%20%2B%5C%20117%5C%20p%5E4q%5C%20r%5C%20s%5C%20%2B%5C%20105%5C%20p%5C%20q%5E3r%5C%20s%5C%20%2B%5C%20260%5C%20p%5E2q%5C%20r%5E2s$

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

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

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

$-%5C%20124%5C%20q%5E5r%5C%20s%5C%20%2B%5C%20196%5C%20p%5E4q%5C%20r%5E2s%5C%20%2B%5C%20590%5C%20p%5C%20q%5E3r%5E2s%5C%20-%5C%20160%5C%20p%5E2q%5C%20r%5E3s%5C%20-%5C%201600%5C%20q%5C%20r%5E4s%5C%20-%5C%2027%5C%20p%5E7s%5E2$

$-%5C%20150%5C%20p%5E4q%5E2s%5E2-%5C%20125%5C%20p%5C%20q%5E4s%5E2-%5C%2099%5C%20p%5E5r%5C%20s%5E2-%5C%20725%5C%20p%5E2q%5E2r%5C%20s%5E2%2B%5C%201200%5C%20p%5E3r%5E2s%5E2%2B%5C%203250%5C%20q%5E2r%5E2s%5E2$

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

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

这四个数 $p%2Cq%2Cr%2Cs$ 拥有以下神奇可爱的性质：

（1）存在一个质数 $m$ ，同时整除这四个数，并且 $m%5E2%5Cnmid%20s$

（2）存在一个质数 $n$ ，同时整除 $A%2CB%2CC%2CD%2CE%2CF$

（3）这四个数恰好使关于x的方程 $x%20%5E5%2Bx%20%5E3p%2Bx%20%5E2q%2Bxr%2Bs%3D0$ 至少有一个根式解

求证： $p%5E2%5Cmid%20F$

在8.1九点前证明者，添加我的微信（主页有），便可得到我的50元奖赏。当然，这题连钓鱼题都不是，ABCDEF看起来太扯淡了，但其实不能算太难吧，需要运用一篇论文的结论（我不信有人能自己没学过就凭空证明出来），提示一下吧，与一元五次方程有关。当然我并没有检验这仨条件是否矛盾，如能指出矛盾者，同样可得奖赏！这道题，当然假设不会有矛盾这样子做就是了。只要您能给出大致的证明，可以直接运用论文结论，方可得到奖赏。另外，只要您和我有共同爱好，就算无法解答、无法推翻我的题目，也可以来和我交流，我急需数学朋友（（（

8.1公布答案，同时会提供论文和相关资料下载链接。欢迎各位持续关注。

标签：数学多项式判别式根式解既约多项式有解条件质数因式分解整除一元五次方程

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