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On the Solutions of an Equation Involving the Smarandache Power Function SP(n) 认领 引用
1
作者 PAN Xiao-wei 《Chinese Quarterly Journal of Mathematics》 北大核心 2008年第3期437-441,共5页
For any positive integer n, the famous Smarandache power function SP（n） is defined as the smallest positive integer m such that n｜m^m, where m and n have the same prime divisors. The main purpose of this paper is u... For any positive integer n, the famous Smarandache power function SP（n） is defined as the smallest positive integer m such that n｜m^m, where m and n have the same prime divisors. The main purpose of this paper is using the elementary methods to study the positive integer solutions of an equation involving the Smarandache power function SP（n） and obtain some interesting results. At the same time, we give an open problem about the related equation. 展开更多
关键词 Smarandache power function equation positive integer solutions
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A Variant of Fermat’s Diophantine Equation 认领 引用 被引量：2
2
作者 Serdar Beji 《Advances in Pure Mathematics》 2021年第12期929-936,共8页
A variant of Fermat’s last Diophantine equation is proposed by adjusting the number of terms in accord with the power of terms and a theorem describing the solubility conditions is stated. Numerically obtained primit... A variant of Fermat’s last Diophantine equation is proposed by adjusting the number of terms in accord with the power of terms and a theorem describing the solubility conditions is stated. Numerically obtained primitive solutions are presented for several cases with number of terms equal to or greater than powers. Further, geometric representations of solutions for the second and third power equations are devised by recasting the general equation in a form with rational solutions less than unity. Finally, it is suggested to consider negative and complex integers in seeking solutions to Diophantine forms in general. 展开更多
关键词 Variant of Fermat’s Last Equation Positive Integer Solutions of New Fermat-Type Equations Geometric Representations for Solutions of New Diophantine Equations
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Heron Triangle and Diophantine Equation 认领 引用
3
作者 YANG Shi-chun MA Chang- wei 《Chinese Quarterly Journal of Mathematics》 北大核心 2005年第3期242-246,共5页
In this paper, we study the quantic Diophantine equation （1） with elementary geometry method, therefore all positive integer solutions of the equation （1） are obtained, and existence of Heron triangle whose median... In this paper, we study the quantic Diophantine equation （1） with elementary geometry method, therefore all positive integer solutions of the equation （1） are obtained, and existence of Heron triangle whose median lengths are all positive integer are discussed here. 展开更多
关键词 quantic Diophantine equation positive integer solution Heron triangle median
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On the Diophantine System a^2+b^2=c^3 and a^x+b^y=c^z for b is an Odd Prime 认领 引用 被引量：4
4
作者 Mao Hua LE 《Acta Mathematica Sinica,English Series》 SCIE 2008年第6期917-924,共8页
Let a, b and c be fixed coprime positive integers. In this paper we prove that if a^2 ＋ b^2 = c^3 and b is an odd prime, then the equation a^x ＋ b^y = c^z has only the positive integer solution （x, y, z） = （2,2,3）.
关键词 exponential diophantine equation positive integer solution generalized Fermat conjecture
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Diophantine equation x2+2m=yn 认领 引用 被引量：7
5
作者 LE Maohua 《Chinese Science Bulletin》 1997年第18期1515-1517,共3页
LET Z,N,Q be the sets of integers,positive integers and rational numbers,respectively.The solutions(x,y,m,n)of the exponential Diophantine equation X^2+2~m=y^n,x,y,m,n∈N,2y,n【2(1)are connected with many questions in... LET Z,N,Q be the sets of integers,positive integers and rational numbers,respectively.The solutions(x,y,m,n)of the exponential Diophantine equation X^2+2~m=y^n,x,y,m,n∈N,2y,n【2(1)are connected with many questions in number theory and combinatorial theory.In the recent fifty years,there were many papers concerned with the equation written by Ljunggren,Nagell,Brown,Toyoizumi and Cohn.In 1986,ref.[1]claimed that all solutions of(1)had been determined.However,we have not seen the proof so far.Therefore,the solution of(1)has not been found yet.In this note,using Baker’s method,we prove the following result. 展开更多
关键词 exponential diophantine equation positive integer solution Baker's method
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