Wyniki wyszukiwania

1

A note on the Diophantine equation $a^x + b^y = c^z$

100%

Cao Z.

Acta Arithmetica

|

1999

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tom 91

|

nr 1

85-93

2

Diophantine equations and class numbers of real quadratic fields

64%

Dong X., Cao Z.

Acta Arithmetica

|

2001

|

tom 97

|

nr 4

313-328

3

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Diophantine equations and class number of imaginary quadratic fields

64%

Cao Z., Dong X.

Discussiones Mathematicae - General Algebra and Applications

|

2000

|

tom 20

|

nr 2

199-206

EN

Let A, D, K, k ∈ ℕ with D square free and 2 ∤ k,B = 1,2 or 4 and $μ_{i} ∈ {-1,1}(i = 1,2)$, and let $h(-2^{1-e}D)(e = 0 or 1)$ denote the class number of the imaginary quadratic field $ℚ(√(-2^{1-e}D))$. In this paper, we give the all-positive integer solutions of the Diophantine equation Ax² + μ₁B = K((Ay² + μ₂B)/K)ⁿ, 2 ∤ n, n > 1 and we prove that if D > 1, then $h(-2^{1-e}D) ≡ 0 (mod n)$, where D, and n satisfy $kⁿ - 2^{e+1} = Dx²$, x ∈ ℕ, 2 ∤ n, n > 1. The results are valuable for the realization of quadratic field cryptosystem.

4

Some classes of Diophantine equations connected with McFarland's and Ma's conjectures

64%

Cao Z., Grytczuk A.

Discussiones Mathematicae - General Algebra and Applications

|

2000

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tom 20

|

nr 2

193-198

EN

In this paper we consider some special classes of Diophantine equations connected with McFarland's and Ma's conjectures about difference sets in abelian groups and we obtain an extension of known results.

5

An application of a lower bound for linear forms in two logarithms to the Terai-Jeśmanowicz conjecture

64%

Cao Z., Dong X.

Acta Arithmetica

|

2003

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tom 110

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nr 2

153-164

6

The simultaneous Pell equations y²-Dz² = 1 and x²-2Dz² = 1

51%

Dong X., Shiu W., Chu C., Cao Z.

Acta Arithmetica

|

2007

|

tom 126

|

nr 2

115-123

Ograniczanie wyników

4 Acta Arithmetica

2 Discussiones Mathematicae - General Algebra and Applications

6 Cao Z.

4 Dong X.

1 Chu C.

1 Grytczuk A.

1 Shiu W.

1 2007

1 2003

1 2001

2 2000

1 1999

A note on the Diophantine equation $a^x + b^y = c^z$

Diophantine equations and class numbers of real quadratic fields

Diophantine equations and class number of imaginary quadratic fields

Some classes of Diophantine equations connected with McFarland's and Ma's conjectures

An application of a lower bound for linear forms in two logarithms to the Terai-Jeśmanowicz conjecture

The simultaneous Pell equations y²-Dz² = 1 and x²-2Dz² = 1