| 关于2个互质整数平方和的研究及其应用 |
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| 引用本文： | 李永,顾志华.关于2个互质整数平方和的研究及其应用[J].河北大学学报(自然科学版),2011,31(6):586-589. |
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| 作者姓名： | 李永 顾志华 |
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| 作者单位： | 1. 河北大学数学与计算机学院,河北保定,071002
2. 河北农业大学理学院,河北保定,071001 |
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| 基金项目： | 河北省自然科学基金资助项目(F2011201063); 保定市社科基金资助项目(20110363) |
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| 摘 要： | 利用无穷下降法和同余式理论,证明了2个互质的整数平方和的任意因数必然也可以表示成为2个整数的平方和,并利用这个结论推论出了Fermat平方定理.
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| 关 键 词： | 整除 互质 同余式 Fermat平方定理 |
About Two Co-prime Integer Square Research and Its Application |
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| LI Yong,GU Zhi-hua.About Two Co-prime Integer Square Research and Its Application[J].Journal of Hebei University (Natural Science Edition),2011,31(6):586-589. |
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| Authors: | LI Yong GU Zhi-hua |
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| Institution: | LI Yong1,GU Zhi-hua2(1.College of Mathematics and Computer Science,Hebei University,Baoding 071002,China,2.College of Science,Agriculture University of Hebei,Baoding 071001,China) |
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| Abstract: | By using infinite descent method and congruent theory,this paper proves that the arbitrary factor of a integer which is a sum of two co-prime integer squares will be necessarily expressed a sum of two co-prime integer squares.This conclusion can deduced the Fermat square theorem. |
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| Keywords: | division co-prime congruent Fermat square theorem |
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