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A note on the Diophantine equation $(a^n x^m ± 1)/(a^n x ± 1) = y^n + 1$

100%

Luo J.

Acta Arithmetica

2000-2001

tom 96

nr 3

223-229

On the Diophantine equation (x² ± C)(y² ± D) = z⁴

63%

Yuan P., Luo J.

Acta Arithmetica

2010

tom 144

nr 1

69-95

Square-classes in Lehmer sequences having odd parameters and their applications

63%

Luo J., Yuan P.

Acta Arithmetica

2007

tom 127

nr 1

49-62

On the diophantine equation $x^y - y^x = c^z$

51%

Zhang Z., Luo J., Yuan P.

Colloquium Mathematicum

2012

tom 128

nr 2

277-285

Applying results on linear forms in p-adic logarithms, we prove that if (x,y,z) is a positive integer solution to the equation $x^y - y^x = c^z$ with gcd(x,y) = 1 then (x,y,z) = (2,1,k), (3,2,k), k ≥ 1 if c = 1, and either $(x,y,z) = (c^k+1,1,k)$, k ≥ 1 or $2 ≤ x < y ≤ max{1.5×10^{10},c}$ if c ≥ 2.

Ograniczanie wyników

3 Acta Arithmetica

1 Colloquium Mathematicum

4 Luo J.

3 Yuan P.

1 Zhang Z.

1 2012

1 2010

1 2007

1 2001

Wyniki wyszukiwania

A note on the Diophantine equation $(a^n x^m ± 1)/(a^n x ± 1) = y^n + 1$

On the Diophantine equation (x² ± C)(y² ± D) = z⁴

Square-classes in Lehmer sequences having odd parameters and their applications

On the diophantine equation $x^y - y^x = c^z$