Polynomial operations: Numerical performance in matrix diophantine equation
Polynomial parametrizations of length 4 Büchi sequences
Polynomial squares of the form
Polynomials dividing infinitely many quadrinomials or quintinomials
Positive solutions of the Diophantine equation.
Power integral bases in orders of composite fields.
Power integral bases in the family of simplest quartic fields.
Power values of sums of products of consecutive integers
We investigate power values of sums of products of consecutive integers. We give general finiteness results, and also give all solutions when the number of terms in the sum considered is at most ten.
Power-free values, large deviations, and integer points on irrational curves
Let be a polynomial of degree without roots of multiplicity or . Erdős conjectured that, if satisfies the necessary local conditions, then is free of th powers for infinitely many primes . This is proved here for all with sufficiently high entropy.The proof serves to demonstrate two innovations: a strong repulsion principle for integer points on curves of positive genus, and a number-theoretical analogue of Sanov’s theorem from the theory of large deviations.
Poznámka o počte riešení optickej rovnice
Poznámka o počte riešení rovnice v prirodzených číslach
p-primary parts of unit traces and the p-adic regulator
Prime divisors of some shifted products.
Prime Pythagorean triangles.
Primes represented by quadratic polynomials in two variables
Primitive divisors of certain elliptic divisibility sequences
Primitive prime factors in second-order linear recurrence sequences
Příspěvek k řešení rovnic neurčitých
Problème de partition
Problème de Waring avec exposant non entier