Add to ORKGMotivated by a question of V. Bergelson and F. K. Richter (2017), we obtain asymptotic formulas for the number of relatively prime tuples composed of positive integers $n\le N$ and integer parts of polynomials evaluated at $n$. The error terms in our formulas depend on the Diophantine properties of the leading coefficients of these polynomials
AbstractLet m ≥ 2, f1, f2,…, fm arbitrary nonconstant polynomials with integer coefficients, and h a...
concerning the upper est’imate of.&f(n) = max N(12,x) = max j 2 p(d) /. * t din d<z Previo...
We show that certain problems involving sparse polynomials with integer coefficients are at least as...
Let f(n) denote the number of relatively prime sets in {1; : : : ; n}. This is sequence A085945 in S...
AbstractLet f(x1, x2,…, xn) be a polynomial with rational integral coefficients. Let d(f) be the gre...
AbstractWe discuss several enumerative results for irreducible polynomials of a given degree and pai...
We find the generating function for the number of k-tuples of monic polynomials of degree n over Fq ...
The Euclidean algorithm for finding greatest common divisors, one of the oldest algorithms in the wo...
Let §P^+ (n) §denote the largest prime factor of the integer §n§ and §P ^+ y (n)§ denote the largest...
We compute the average orders and study the distribution of values of a class of divisor functions d...
AbstractIf A is a set of positive integers, we denote by p(A,n) the number of partitions of n with p...
In this thesis, we will study a class of divisor functions: the prime symmetric functions. These are...
The Fundamental Theorem of Arithmetic is usually stated in a form emphasizing how primes enter the s...
We show that if two monic polynomials with integer coefficients have a square-free resultant, then a...
Let p(n) denote the number of partitions of the integer n. The first exact formula for p(n) was publ...
AbstractLet m ≥ 2, f1, f2,…, fm arbitrary nonconstant polynomials with integer coefficients, and h a...
concerning the upper est’imate of.&f(n) = max N(12,x) = max j 2 p(d) /. * t din d<z Previo...
We show that certain problems involving sparse polynomials with integer coefficients are at least as...
Let f(n) denote the number of relatively prime sets in {1; : : : ; n}. This is sequence A085945 in S...
AbstractLet f(x1, x2,…, xn) be a polynomial with rational integral coefficients. Let d(f) be the gre...
AbstractWe discuss several enumerative results for irreducible polynomials of a given degree and pai...
We find the generating function for the number of k-tuples of monic polynomials of degree n over Fq ...
The Euclidean algorithm for finding greatest common divisors, one of the oldest algorithms in the wo...
Let §P^+ (n) §denote the largest prime factor of the integer §n§ and §P ^+ y (n)§ denote the largest...
We compute the average orders and study the distribution of values of a class of divisor functions d...
AbstractIf A is a set of positive integers, we denote by p(A,n) the number of partitions of n with p...
In this thesis, we will study a class of divisor functions: the prime symmetric functions. These are...
The Fundamental Theorem of Arithmetic is usually stated in a form emphasizing how primes enter the s...
We show that if two monic polynomials with integer coefficients have a square-free resultant, then a...
Let p(n) denote the number of partitions of the integer n. The first exact formula for p(n) was publ...
AbstractLet m ≥ 2, f1, f2,…, fm arbitrary nonconstant polynomials with integer coefficients, and h a...
concerning the upper est’imate of.&f(n) = max N(12,x) = max j 2 p(d) /. * t din d<z Previo...
We show that certain problems involving sparse polynomials with integer coefficients are at least as...