On indefinite quadratic forms in four variables
On integer solutions to x² - dy² = 1, z² - 2dy² =1
On integral similitude matrices
We study integral similitude 3 × 3-matrices and those positive integers which occur as products of their row elements, when matrices are symmetric with the same numbers in each row. It turns out that integers for which nontrivial matrices of this type exist define elliptic curves of nonzero rank and are closely related to generalized cubic Fermat equations.
On Krasner's Criteria for the First Case of Fermat's Last Theorem.
On Krasnér's theorem for the first case of Fermat's last theorem
On Lucas and Lehmer sequences and their applications to Diophantine equations
On minimal solutions of Diophantine equations.
On mod logarithms and .
On nonary cubic forms: II.
On nonary cubic forms: III.
On Obláth's problem.
On -adic zeros of systems of diagonal forms restricted by a congruence condition
This paper is concerned with non-trivial solvability in -adic integers of systems of additive forms. Assuming that the congruence equation has a solution with we have proved that any system of additive forms of degree with at least variables, has always non-trivial -adic solutions, provided . The assumption of the solubility of the above congruence equation is guaranteed, for example, if .
On pairs of additive cubic equations.
On pairs of binary forms with given resultant or given semi-resultant.
On perfect powers in products with terms from arithmetic progressions
On Perrine's generalized Markoff equation.
On Perrine's generalized Markoff equations. (Summary).
On Pillai's Diophantine equation.
On polynomial-exponential equations.
On polynomials that are sums of two perfect qth powers