Inhomogeneous norm form equations over function fields
Integer Points and the Rank of Thue Elliptic Curves.
Integer Points on Curves and Surfaces.
Integer points on curves of genus 1
Integer Points on Hypersurfaces.
Integer solutions of a sequence of decomposable form inequalities
Integer solutions of some Diophantine equations via Fibonacci and Lucas numbers.
Integers representable by .
Integers with identical digits
Integer-valued quadratic forms and quadratic Diophantine equations.
Integral Points on Certain Elliptic Curves
Integral points on elliptic curves defined by simplest cubic fields.
Integral points on the elliptic curve
Let be a fixed odd prime. We combine some properties of quadratic and quartic Diophantine equations with elementary number theory methods to determine all integral points on the elliptic curve . Further, let denote the number of pairs of integral points on with . We prove that if , then or depending on whether or .
Intermediate values and inverse functions on non-Archimedean fields.
Iterated exponents in number theory.
Iterated Ring Class Fields and the 168-Tesselation.
Iterated Ring Class Fields and the Icosahedron.
Jacobi symbols, ambiguous ideals, and continued fractions
The purpose of this paper is to generalize some seminal results in the literature concerning the interrelationships between Legendre symbols and continued fractions. We introduce the power of ideal theory into the arena. This allows significant improvements over the existing results via the infrastructure of real quadratic fields.
Jednoduché nové řešení diofantické rovnice
Jeśmanowicz' conjecture with congruence relations
Let a,b and c be relatively prime positive integers such that a²+b² = c². We prove that if and for some non-negative integer r, then the Diophantine equation has only the positive solution (x,y,z) = (2,2,2). We also show that the same holds if c ≡ -1 (mod a).