查看“︁School:李煌數學研究院/举出一个非平凡存在根式解的代数方程”︁的源代码

== 李煌定理==

已知费马方程<math>a^n+b^n=c^n</math>成立

则等式<math>c^{7n}=\frac{1}{16}(-2(-c^{4n}(  8 c^{n}  +22   c^{2n}   +28  c^{3n} -41c^{4n}-38  c^{5n} +2c^{6n}  +12)b^n+ </math> <math>      3   c^{4n}(-26   c^{2n} -28  c^{3n}+7 c^{4n}    +2  c^{5n}   -4)b^{2n}+</math><math>  2c^{2n}(52c^{2n}+56c^{3n}-44c^{4n}-24c^{5n}+c^{6n}+8)b^{3n}-</math><math>    20c^{4n}(  -6c^n+    c^{2n} -9   )b^{4n}+24c^{2n}(  -4c^n+    3c^{2n} -6  )b^{5n}-</math><math>    112c^{2n}b^{6n}+64b^{7n}+c^{6n}(2c^{2n}+6c^{2n}+7c^{3n}-7c^{4n}-6c^{5n}+3))a^n+</math><math>     (-6c^{4n}(-26c^{2n}-28c^{3n}+7c^{4n}+2c^{5n}-4)b^n-</math><math>     6c^{2n}(52c^{2n}+56c^{3n}-44c^{4n}-24c^{5n}+c^{6n}+8)b^{2n}+80c^{4n}</math><math>        (-6c^n+c^{2n}-9)b^{3n}-120c^{2n}(-4c^n+3c^{2n}-6)b^{4n}+672c^{2n}b^{5n}-</math><math>         448b^{6n}+c^{4n}(  8 c^{n}  +22   c^{2n}   +28  c^{3n} -41c^{4n}-38  c^{5n} +2c^{6n}  +12))a^{2n}-</math><math>       2(2c^{2n}(52c^{2n}+56c^{3n}-44c^{4n}-24c^{5n}+c^{6n}+8)b^{n}-</math><math>     40c^{4n}(-6c^n+    c^{2n} -9   )b^{2n}+80c^{2n}(  -4c^n+    3c^{2n} -6  )b^{3n}-</math><math>       560c^{2n}b^{4n}+448b^{5n}+c^{4n}(-26   c^{2n} -28  c^{3n}+7 c^{4n}    +2  c^{5n}   -4))a^{3n}-</math><math>    (-40c^{4n}(  -6c^n+    c^{2n} -9   )b^{n}+120c^{2n}(  -4c^n+    3c^{2n} -6  )b^{2n}-1120c^{2n}b^{3n}+</math><math>         1120b^{4n}+c^{2n}(52c^{2n}+56c^{3n}-44c^{4n}-24c^{5n}+c^{6n}+8))a^{4n}-</math><math>        8(6c^{2n}(-4c^n+3c^{2n}-6)b^{n}-84c^{2n}b^{2n}+112b^{3n}+  c^{4n}   (6c^n-c^{2n}+9))a^{5n}-</math><math>         8(-28c^{2n}b^{n}+56b^{2n}+c^{2n}(-4c^n+3c^{2n}-6))a^{6n}-</math><math>        32(  4b^n-c^{2n}   )a^{7n}-16a^{8n} +32b^{7n}c^{2n}-</math><math>       16b^{8n}+8b^{5n}c^{4n}(-6c^{n}+c^{2n}-9)-</math><math>     8b^{6n}c^{2n}(-4c^{n}+3c^{2n}-6)+</math><math>       2b^{n}c^{6n}(-2c^{n}-6c^{2n}-7  c^{3n}+7c^{4n}+ 6c^{5n}-3   )+</math><math>     c^{6n}(6c^{n}+2c^{2n}-4  c^{3n}+27c^{4n}+ 6c^{5n}-9 c^{6n}-4   )-</math><math>       b^{4n}c^{2n}(52c^{2n}+56c^{3n}-44c^{4n}-24c^{5n}+c^{6n}+8 )+</math><math>      b^{2n}c^{4n}(8c^{n}+22c^{2n}+28c^{3n}-41c^{4n}-38c^{5n}+2c^{6n}+12 )+</math><math>    b^{3n}(8c^{4n}+52c^{6n}+56c^{7n}     -14c^{8n}-4c^{9n}))</math>

也成立

== 参考 ==
* 《南昌理工學院學報》.李煌


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