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Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 31-33 (2009).

MSC: 11A25

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Wang, Chunping; Zhao, Yanlin

On an equation involving the Smarandache function and the Dirichlet divisor function. (English) Zbl 1219.11007

Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 27-30 (2009).

MSC: 11A25

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Li, Fanbei

A functional equation related to the Smarandache function and its positive integer solutions. (Chinese. English summary) Zbl 1199.11012

J. Northwest Univ., Nat. Sci. Ed. 38, No. 6, 892-894 (2008).

MSC: 11A25

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Zhang, Wenpeng

On two problems of the Smarandache function. (Chinese. English summary) Zbl 1199.11033

J. Northwest Univ., Nat. Sci. Ed. 38, No. 2, 173-176 (2008).

MSC: 11A25

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Zhu, Minhui

An equation involving the Smarandache function and its positive integer solutions. (English) Zbl 1199.11036

Sci. Magna 4, No. 4, 1-3 (2008).

MSC: 11A25

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Cheng, Bin

On the pseudo Smarandache square-free function. (English) Zbl 1199.11006

Sci. Magna 4, No. 2, 21-24 (2008).

MSC: 11A25

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Zhang, Pei

An equation involving the pseudo-Smarandache squarefree function. (Chinese. English summary) Zbl 1199.11032

J. Zhengzhou Univ., Nat. Sci. Ed. 40, No. 2, 36-38 (2008).

MSC: 11A25

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Cai, Lixiang

An equation involving an arithmetic function and its positive integer solution. (Chinese. English summary) Zbl 1199.11004

J. Zhengzhou Univ., Nat. Sci. Ed. 40, No. 2, 33-35 (2008).

MSC: 11A25

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Liang, Ming; Le, Maohua

On the Diophantine equation \( (n+1)+ (n+2)^y=n^z\). (Chinese. English summary) Zbl 1199.11082

Pure Appl. Math. 24, No. 4, 736-741 (2008).

MSC: 11D61

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Lin, Muyuan

On the Schinzel-Sierpiński equation. (Chinese. English summary) Zbl 1174.11369

J. Math., Wuhan Univ. 28, No. 3, 287-289 (2008).

MSC: 11D25

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Yan, Xiaoxia

An equation involving the pseudo-Smarandache function and the Smarandache multiplicative function. (Chinese. English summary) Zbl 1174.11334

Pure Appl. Math. 24, No. 2, 372-374 (2008).

MSC: 11A99

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Le, Maohua

On the Diophantine system \(a^2+ b^2 = c^3\) and \(a^x + b^y = c^z\) for \(b\) is an odd prime. (English) Zbl 1218.11037

Acta Math. Sin., Engl. Ser. 24, No. 6, 917-924 (2008).

Reviewer: Olaf Ninnemann (Berlin)

MSC: 11D61

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Found 131 Documents (Results 1–100)

On the Diophantine equation \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{n}\). (English) Zbl 07663621

A Diophantine equation and its positive integer solutions. (English) Zbl 1513.11118

Perfect powers of five with few ternary digits. (Chinese. English summary) Zbl 1513.11102

On the positive integer solutions of the simultaneous Diophantine equations \(8{x^2} - 6{y^2} = 2\) and \(28{y^2} - 8{z^2} = 20\). (Chinese. English summary) Zbl 1488.11080

The positive integer solutions to multivariate Euler function equation \(\varphi(x_1x_2 \cdots x_n) = k_1\varphi(x_1) + k_2\varphi(x_2) + \cdots + k_n\varphi(x_n) \pm l\). (Chinese. English summary) Zbl 1488.11014

The solutions of arithmetic function equation \(k\varphi(Y) = {\varphi_2}(Y) + S(Y^8)\). (Chinese. English summary) Zbl 1488.11013

Discussion on the positive integer solution of equation \(k\varphi (m) = S(m^t)\). (Chinese. English summary) Zbl 1488.11012

A conjecture of Jeśmanowicz concerning Pythagorean triples. (Chinese. English summary) Zbl 1488.11092

A variety of Euler’s sum of powers conjecture. (English) Zbl 07442476

On the Diophantine equation \(7x(x + 1)(x + 2)(x + 3) = 5y(y + 1)(y + 2)(y + 3)\). (Chinese. English summary) Zbl 1488.11083

Number of solutions to \({(an)^x} + {(bn)^y} = {(cn)^z}\). (Chinese. English summary) Zbl 1488.11091

On the Diophantine equation \(X^2 - (a^2 + 1)Y^4 = k^2 - 1 - 2ka\). (Chinese. English summary) Zbl 1488.11081

On products of consecutive arithmetic progressions. III. (English) Zbl 1480.11035

On the Diophantine equation \((2^x-1)(p^y-1)=2z^2\). (English) Zbl 1513.11115

The solvability of the equation \({\varphi_e}(n) = {p^{t\omega (n)}}(e = 2, 3, 4, 6)\). (Chinese. English summary) Zbl 1474.11008

The positive integer solutions of elliptic curves \({y^2} = qx ({x^2} - 256)\). (Chinese. English summary) Zbl 1474.11087

The solution of a quaternary variable coefficient mixed equation on Euler function \(\varphi (n)\). (Chinese. English summary) Zbl 1474.11019

Diophantine equation \(((c + 1)m^2 + 1)^x + (cm^2 - 1)^y = (am)^z\). (Chinese. English summary) Zbl 1474.11095

Discussion of solutions of an equation on the number-theoretic function \(\varphi(m)\). (Chinese. English summary) Zbl 1463.11107

Extension of the Stormer theorem. (Chinese. English summary) Zbl 1463.11100

The solvability of the equation \({\varphi_e} (n) = 2^{t\omega (n)}\). (Chinese. English summary) Zbl 1463.11006

On the Diophantine equation \(x^2-2y^4=M (M=17, 41, 73, 89, 97)\). (Chinese. English summary) Zbl 1463.11103

On the positive integer solution of a ternary variable coefficient Euler function equation. (Chinese. English summary) Zbl 1463.11013

On the Diophantine equation \(X^2 + 4Y^4 = pZ^4\). (Chinese. English summary) Zbl 1449.11057

Solvability of a ternary variable coefficient of Euler functional equation with constant terms and a perfect number. (Chinese. English summary) Zbl 1449.11009

On the positive integer solution of Diophantine equation \(x (x+1) (x+2) (x+3) = 42y (y+1) (y+2) (y+3)\). (Chinese. English summary) Zbl 1449.11058

The solvability of the equation \(Z (n) = \varphi_e(\mathrm{SL}(n))\). (Chinese. English summary) Zbl 1449.11016

The exponential Diophantine equation \((3am^2-1)^x+(a(a-3)m^2+1)^y=(am)^z\). (English) Zbl 1448.11071

Two equations on generalized Euler function \({\varphi_2} (n)\). (Chinese. English summary) Zbl 1449.11015

Solutions on Euler function equation \(\varphi (n) = {2^{\omega (n)}}{3^{\omega (n)}}{5^{\omega (n)}}\). (Chinese. English summary) Zbl 1449.11014

Solutions of two equations related to generalized Euler function. (Chinese. English summary) Zbl 1449.11013

On the exponential Diophantine equation \(x^2=D^{2m}-D^mP^n+p^{2n}\). (Chinese. English summary) Zbl 1438.11085

On positive integer solutions to the simultaneous Pell equations \({y^2} - D{z^2} = 1\), \({x^2} - 2D{z^2} = 1\). (Chinese. English summary) Zbl 1438.11076

Several nonlinear equations on Euler function \(\varphi(n)\). (Chinese. English summary) Zbl 1438.11013

Solutions of two equations mixing Euler function \(\varphi(n)\) with generalized Euler function \(\varphi_2(n)\). (Chinese. English summary) Zbl 1438.11011

A note on the Goormaghtigh equation. (English) Zbl 1438.11089

A mixed integer programming approach to the tensor complementarity problem. (English) Zbl 1425.90072

The solvability for a class of the exponential Diophantine equation. (Chinese. English summary) Zbl 1424.11085

Existence of solution for the system of Pell equations. (Chinese. English summary) Zbl 1424.11071

Positive integer solutions of a nonlinear equation containing Euler function \(\varphi (n)\). (Chinese. English summary) Zbl 1424.11010

Positive integer solution of nonlinear equations related to Euler function \(\varphi \left ( n \right)\). (Chinese. English summary) Zbl 1424.11018

On the Diophantine equation \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{3p}\). (English) Zbl 1425.11061

On the solvability of the cubic Diophantine equation \({x^3}+1=2{p_1}{p_2}Q{y^2}\). (Chinese. English summary) Zbl 1399.11094

Several equations related to the Euler function \(\varphi \left ( n \right)\). (Chinese. English summary) Zbl 1399.11058

On the Diophantine system \(f(z)= f(x) f(y)= f(u) f(v)\). (English) Zbl 1387.11024

On the Diophantine equation \(y(y + 1)(y + 2)(y + 3) = n^2x(x + 1)(x + 2)(x + 3)\). (Chinese. English summary) Zbl 1389.11080

A note on the exponential Diophantine equation \((am^2+1)^x+(bm^2-1)^y=(cm)^z\). (English) Zbl 1425.11058

On the Diophantine equation \(p^x + (p + 1)^y =z^2\). (Chinese. English summary) Zbl 1389.11090

The positive integer solutions of Diophantine equation \(\varphi(xyz) = 5(\varphi(x) + \varphi(y) + \varphi(z))\). (Chinese. English summary) Zbl 1374.11005

On the solvability of the equation \(\varphi_e(n) = \frac{n}{d}\) \((e = 1, 2, 4)\). (Chinese. English summary) Zbl 1374.11011

The number of solutions of the generalized Ramanujan-Nagell equation \(x^2+D^m=4p^n\). (Chinese. English summary) Zbl 1374.11059

On the positive integer solutions of a class of generalized Ramanujan-Nagell equation. (Chinese. English summary) Zbl 1374.11046

Three kinds of equations involving Euler function. (Chinese. English summary) Zbl 1363.11033

On the Diophantine equation \(x^2-kxy+ y^2 + px = 0\). (Chinese. English summary) Zbl 1363.11050

Positive integer solutions of Mordell’s equation \(y^3 = x^2 + 2p^4\). (Chinese. English summary) Zbl 1363.11052

All solutions of the Diophantine equation \(x^2 +2^m = y^n\). (Chinese. English summary) Zbl 1349.11075

An equation involving the Smarandache LCM dual function. (Chinese. English summary) Zbl 1349.11003

On Terai’s conjecture concerning the Diophantine equation \(a^x +b^y= c^z\). (Chinese. English summary) Zbl 1349.11074

The necessary conditions for the equation \(x^3+1=3py^2\) having positive integer solutions. (Chinese. English summary) Zbl 1340.11034

A note on the exponential Diophantine equation \((4m^2+1)^x+(5m^2-1)^y=(3m)^z\). (English) Zbl 1364.11087

On the Diophantine system \(a^2+b^2=c^r\) and \(a^x+b^y=c^z\) for \(b\) is a prime. (English) Zbl 1339.11047

The upper bound for solutions of the generalized Brocard-Ramanujan equation \(x^2-D=y!\). (Chinese. English summary) Zbl 1324.11032

On the Diophantine equation \(2^yn^{y-x}=(b+2)^x-b^x\). (Chinese. English summary) Zbl 1313.11072

A note on the ternary pure exponential Diophantine equations. (Chinese. English summary) Zbl 1313.11073

The criteria for the equation \(x^3-1=2py^2\) having positive integer solutions. (Chinese. English summary) Zbl 1313.11064

On the Diophantine equation \(p^{2m}-Dx^2=1\). (Chinese. English summary) Zbl 1313.11074

The criteria for the equation \(x^3-8=py^2\) has primitive positive integer solutions. (Chinese. English summary) Zbl 1313.11061

On the Diophantine equation \(x(x+1)(x+2)=2p^ky^n\). (Chinese. English summary) Zbl 1313.11063

On the Diophantine equation \(x^3\pm 1=pD_1y^2\). (Chinese. English summary) Zbl 1313.11059

A kind of an exponential Diophantine system and its integer solution. (Chinese. English summary) Zbl 1299.11036

An equation involving Smarandache function \(S(n)\) and pseudo Smarandache function \(Z_1(n)\) and its positive integer solutions. (Chinese. English summary) Zbl 1289.11003

On the cubic Diophantine equation \(x^3+1=3py^2\). (Chinese. English summary) Zbl 1274.11083

On the Diophantine equation \((20n)^x+(21n)^y=(29n)^z\). (English) Zbl 1274.11088

On the solutions of the exponential Diophantine equation \(a^x+b^y=(m^2+1)^z\). (English) Zbl 1274.11086

An equation involving the L.C.M. product of the arithmetical function. (Chinese. English summary) Zbl 1274.11010

An equation involving the Smarandache function and the pseudo-Smarandache function of second kind. (Chinese. English summary) Zbl 1249.11043