A quantitative version of Runge's theorem on diophantine equations
On integer solutions to x² - dy² = 1, z² - 2dy² =1
Corrections to "A quantitative version of Runge's theorem on diophantine equations" (Acta Arith. 62 (1992), 157-172)
Sharp bounds for the number of solutions to simultaneous Pellian equations
On the number of large integer points on elliptic curves
On unit solutions of the equation xyz = x+y+z in the ring of integers of a quadratic field
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
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.
On the Diophantine equation x² - dy⁴ = 1 with prime discriminant II
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...
Addendum on the equation aX⁴ - bY² = 2
Solving a family of Thue equations with an application to the equation x²-Dy⁴=1
On the equation aX⁴-bY² = 2
On the Diophantine equation
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