Wyniki wyszukiwania

1

Sharp bounds for the number of solutions to simultaneous Pellian equations

100%

Walsh P.

Acta Arithmetica

|

2007

|

tom 126

|

nr 2

125-137

2

Corrections to "A quantitative version of Runge's theorem on diophantine equations" (Acta Arith. 62 (1992), 157-172)

100%

Walsh P.

Acta Arithmetica

|

1995

|

tom 73

|

nr 4

397-398

3

On integer solutions to x² - dy² = 1, z² - 2dy² =1

100%

Walsh P.

Acta Arithmetica

|

1997

|

tom 82

|

nr 1

69-76

4

A quantitative version of Runge's theorem on diophantine equations

100%

Walsh P.

Acta Arithmetica

|

1992

|

tom 62

|

nr 2

157-172

5

On the number of large integer points on elliptic curves

100%

Walsh P.

Acta Arithmetica

|

2009

|

tom 138

|

nr 4

317-327

6

On the Diophantine equation x² - dy⁴ = 1 with prime discriminant II

64%

Poulakis D., Walsh P.

Colloquium Mathematicum

|

2006

|

tom 105

|

nr 1

51-55

EN

Let p denote a prime number. P. Samuel recently solved the problem of determining all squares in the linear recurrence sequence {Tₙ}, where Tₙ and Uₙ satisfy Tₙ² - pUₙ² = 1. Samuel left open the problem of determining all squares in the sequence {Uₙ}. This problem was recently solved by the authors. In the present paper, we extend our previous joint work by completely solving the equation Uₙ = bx², where b is a fixed positive squarefree integer. This result also extends previous work of the second author.

7

On a Diophantine problem of Bennett

64%

Hai Y., Walsh P.

Acta Arithmetica

|

2010

|

tom 145

|

nr 2

129-136

8

Squares in Lehmer sequences and some Diophantine applications

64%

Luca F., Walsh P.

Acta Arithmetica

|

2001

|

tom 100

|

nr 1

47-62

9

On the number of nonquadratic residues which are not primitive roots

64%

Luca F., Walsh P.

Colloquium Mathematicum

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2004

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tom 100

|

nr 1

91-93

EN

We show that there exist infinitely many positive integers r not of the form (p-1)/2 - ϕ(p-1), thus providing an affirmative answer to a question of Neville Robbins.

10

On the Diophantine equation $X^2 - (2^{2m}+1)Y^4 = -2^{2m}$

52%

Stoll M., Walsh P., Yuan P.

Acta Arithmetica

|

2009

|

tom 139

|

nr 1

57-63

11

Solving a family of Thue equations with an application to the equation x²-Dy⁴=1

52%

Togbe A., Voutier P., Walsh P.

Acta Arithmetica

|

2005

|

tom 120

|

nr 1

39-58

12

On the equation aX⁴-bY² = 2

52%

Akhtari S., Togbé A., Walsh P.

Acta Arithmetica

|

2008

|

tom 131

|

nr 2

145-169

13

Addendum on the equation aX⁴ - bY² = 2

52%

Akhtari S., Togbé A., Walsh P.

Acta Arithmetica

|

2009

|

tom 137

|

nr 3

199-202

Ograniczanie wyników

11 Acta Arithmetica

2 Colloquium Mathematicum

13 Walsh P.

2 Akhtari S.

2 Luca F.

2 Togbé A.

1 Hai Y.

1 Poulakis D.

1 Stoll M.

1 Togbe A.

1 Voutier P.

1 Yuan P.

1 2010

3 2009

1 2008

1 2007

1 2006

1 2005

1 2004

1 2001

1 1997

1 1995

1 1992

Sharp bounds for the number of solutions to simultaneous Pellian equations

Corrections to "A quantitative version of Runge's theorem on diophantine equations" (Acta Arith. 62 (1992), 157-172)

On integer solutions to x² - dy² = 1, z² - 2dy² =1

A quantitative version of Runge's theorem on diophantine equations

On the number of large integer points on elliptic curves

On the Diophantine equation x² - dy⁴ = 1 with prime discriminant II

On a Diophantine problem of Bennett

Squares in Lehmer sequences and some Diophantine applications

On the number of nonquadratic residues which are not primitive roots

On the Diophantine equation $X^2 - (2^{2m}+1)Y^4 = -2^{2m}$

Solving a family of Thue equations with an application to the equation x²-Dy⁴=1

On the equation aX⁴-bY² = 2

Addendum on the equation aX⁴ - bY² = 2