Generalization of the formula of Faa di Bruno for a composite function with a vector argument.
How to explicitly solve a Thue-Mahler equation
Index form equations in quintic fields
The problem of determining power integral bases in algebraic number fields is equivalent to solving the corresponding index form equations. As is known (cf. Győry [25]), every index form equation can be reduced to an equation system consisting of unit equations in two variables over the normal closure of the original field. However, the unit rank of the normal closure is usually too large for practical use. In a recent paper Győry [27] succeeded in reducing index form equations to systems of unit...
Index form equations in sextic fields: a hard computation
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 .
Lower bounds for perfect rational cuboids
Note on a theorem of Rockett and Szusz on a diophantine equation x² - dy² = N
On elliptic diophantine equations that defy Thue's method: The case of the Ochoa curve.
On power values of pyramidal numbers, I
On some properties of two simultaneous polygonal sequences.
On square values of quadratics
On the congruence modulo .
On the diophantine equation
In this paper, we find all integer solutions of the equation in the title for non-negative integers and under the condition that the integers and are relatively prime and . The proof depends on the famous primitive divisor theorem due to Bilu, Hanrot and Voutier and the computational techniques on some elliptic curves.
On the Diophantine equation
In this paper, we find all solutions of the Diophantine equation in positive integers , with .
On the Diophantine equation
On the elliptic logarithm method for elliptic Diophantine equations: reflections and an improvement.
On the Lebesgue-Nagell equation
We completely solve the Diophantine equations (for q = 17, 29, 41). We also determine all and , where are fixed primes satisfying certain conditions. The corresponding Diophantine equations x² + C = yⁿ may be studied by the method used by Abu Muriefah et al. (2008) and Luca and Togbé (2009).
On the resolution of simultaneous Pell equations.
Power integral bases in the family of simplest quartic fields.