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  A Counter Example of Fermat Last Theorem          Wang Shiqiang               (School of Mathematics,Beijing Normal University,100875 Beijing)          Abstract: In this paper we prove by Model-Theoretic method that there exist a Counter Example of Fermat Last Theorem  Keywords: Fermat Last Theorem,Model Theory.                                        Firstly we see: 16+16=16 in the Residue Class Ring I/(16) of the Integer Ring I modulo 16 and 2 is nonzero in I/(16);81+81=81 in I/(81)and 3 is nonzero in I/(81); 256+256=256 in I/(256)and 4 is nonzero in I/(256);.................                                  Now we will prove:                   Theorem.There exist a Counter Example to Fermat Last Theorem.     Proof.We write the above modules 16,81,256,...............by n1,n2,n3,... ............                                       We will denote Peano Axioms by PA briefly and rewrite the following axiom:“(for all n)[n+1?0] ”into:“{0+1?0, 1+1?0, 2+1?0, ......,n+1?0, ...........} (n runs over all natural numbers) ”.                                We use FE(n) to denote the Fermat Equation in Fermat Last Theorem for index n. Now consider the following infinite set of sentences:U={PA;(exist n)[(n>2 in PA) and (FE(n) has nontrivial solutions in PA) and (n=0)]---(Q)}.                                For any finite subset V of U,it is easily seen that there is some Residue Class Ring I/(nk) of the Integer Ring I modulo nk which satisfy V; Hence by the Compactness Theorem of Model Theory we know that U itself has a model M. Let us look at M: As M satisfies (Q),we see that FE(n) has nontrivial solutions in M.But M satisfies PA, so we see that FE(n) has nontrivial solutions in PA.

Fermat 大定理的一个反例。?王世强（北京师范大学数学学院，100875 北京）摘要。本文用模型论方法证明：存在Fermat大定理的反例。关鍵词。Fermat大定理，模型论。作者简介:王世强（1927-）.1948年毕业于北京师范大学数学系后留系工作,1981年被评为博士导师.已发表论文百余篇.已出版:<模型论基础>(科学出版社, 1987),<王世强文集>(北

刚才我写的日志中,G是说Goldbach猜想.我在<前沿科学>今年第1期已发表了一篇关于Clifford数的Goldbach猜想的证明(Clifford数是一种比普通整数复杂一些的八元数.可参看<数学通报>2009年第4期李邦河院士的介绍文章)是由我出想法,请友人史璟博士具体写出投稿的.仿照此文,就可证明通常的Goldbach猜想.证明将在<前沿科学>今年第4期登出.王世强

有一位胡思之先生批评我关于G猜想的文章.虽然批评,但未见胡先生是否也在这方面作过研究?各位若有人知道他的邮箱或电话,请告诉我.极为感谢!王世强