On Wendt's determinant and Sophie Germain's theorem.
On Weyl's inequality and Waring's problem for cubes
On and
The two related Diophantine equations: and , have infinitely many nontrivial, primitive integral solutions. We give two parametric solutions, one for each of these equations.
On
In p. 219 of R.K. Guy’s Unsolved Problems in Number Theory, 3rd edn., Springer, New York, 2004, we are asked to prove that the Diophantine equation has no integer solutions with and . But, contrary to this expectation, we show that for , this equation has infinitely many primitive integer solutions, i.e. the solutions satisfying the condition .
On x³ + y³ + z³ = 3μxyz and Jacobi polynomials
On zeros of diagonal forms over p-adic fields
On zeros of forms over local fields
One Erdös style inequality
One unusual inequality is examined.
Original title unknown
Orthant spanning simplexes with minimal volume.
Osservazioni sul problema di Fermat.
Pairs of additive equations IV. Sextic equations
Pairs of additive equations of small degree
Pairs of additive forms and Artin's conjecture
Pairs of cubic forms in many variables
Pairs of Pell equations having at most one common solution in positive integers.
Palindromic powers.
Parametric solutions for some Diophantine equations.
Parametric Solutions of the Diophantine Equation A² + nB⁴ = C³
The Diophantine equation A² + nB⁴ = C³ has infinitely many integral solutions A, B, C for any fixed integer n. The case n = 0 is trivial. By using a new polynomial identity we generate these solutions, and then give conditions when the solutions are pairwise co-prime.
Parametrization of integral values of polynomials
We will recall a recent result about the classification of those polynomial in one variable with rational coefficients whose image over the integer is equal to the image of an integer coefficients polynomial in possibly many variables. These set is polynomially generated over the integers by a family of polynomials whose denominator is and they have a symmetry with respect to a particular axis.We will also give a description of the linear factors of the bivariate separated polynomial over a...