==李煌定理==
<math>y^3=48x^4+16x^6</math> 仅有整数解(0,0),(1,4),(-1,4)
证明:
因为李煌恒等式:<math>{(2x-2)}^{3}+{(2x+2)}^3={(48{x}+{16x^3})}</math>
证毕.
==李煌定理==
<math>x^3=6y^2+2</math> 仅有整数解(2,1),(2,-1)
证明(proof):
<math>{(1-y)}^{12}+{(1-y)^9}{(1+y)^3}={(1-y)}^9{(6y^2+2)}</math>
证毕(end.)
==李煌定理==
如果代數幾何曲線不定方程 <math>z^n=x^n+y^n,3\nmid n</math>有正整數解(x,y,z,n)
则代數幾何曲線不定方程:<math>a^3+b^3=c{d^3}</math>有正整數解(a,b,c,d)
==参考文献==
[http://www.baike.com/wiki/%E6%A4%AD%E5%9C%86%E6%9B%B2%E7%BA%BF]
== 來源 ==
* 《南昌理工學院學報》.李煌
* http://www.mftp.info/20140202/1392101138x1873735091.jpg
<<[[School:李煌數學研究院]]
[[Category:ZH]]
[[Category:李煌數學研究院]]
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