AbstractWe estimate the number of solutions of certain congruences with Catalan numbers and middle binomial coefficients modulo a prime. We use these results to bound double exponential sums with products of two Catalan numbers and two middle binomial coefficients, respectively, which in turn lead us to upper bounds on single exponential sums
In this paper, we find all the solutions of the title Diophantine equation in positive integers (m, ...
We show that the equation $\frac{x^p + y^p}{x+y} = p^e z^q$ has no solutions in coprime integers $x,...
AbstractFor a real x ≥ 1 we denote by S[x] the set of squarefull integers n ≤x, that is, the set of ...
AbstractWe estimate the number of solutions of certain congruences with Catalan numbers and middle b...
We obtain new bounds of exponential sums modulo a prime p with binomials axk + bxn. In particular, ...
AbstractWe estimate character sums with Catalan numbers and middle binomial coefficients modulo a pr...
This is a preprint of a book chapter published in High Primes and Misdemeanours: Lectures in Honour ...
AbstractWe prove various congruences for Catalan and Motzkin numbers as well as related sequences. T...
AbstractLet b⩾2 be a fixed positive integer and let S(n) be a certain type of binomial sum. In this ...
© Foundation Compositio Mathematica 2004. Cambridge Journals. doi: 10.1112/S0010437X03000022.We give...
AbstractWe prove by the theory of algebraic numbers a result (Theorem 3) which, together with our ea...
Motivated by recently developed interest to the distribution of $q$-arydigits of Mersenne numbers $M...
http://www.math.missouri.edu/~bbanks/papers/index.htmlLet p be a prime and 79 an integer of order t ...
AbstractFor a fixed integer s≥2, we estimate exponential sums with alternative power sums As(n)=∑i=0...
Abstract. Let p be a prime and V an integer of order t in the multiplicative group modulo p. In this...
In this paper, we find all the solutions of the title Diophantine equation in positive integers (m, ...
We show that the equation $\frac{x^p + y^p}{x+y} = p^e z^q$ has no solutions in coprime integers $x,...
AbstractFor a real x ≥ 1 we denote by S[x] the set of squarefull integers n ≤x, that is, the set of ...
AbstractWe estimate the number of solutions of certain congruences with Catalan numbers and middle b...
We obtain new bounds of exponential sums modulo a prime p with binomials axk + bxn. In particular, ...
AbstractWe estimate character sums with Catalan numbers and middle binomial coefficients modulo a pr...
This is a preprint of a book chapter published in High Primes and Misdemeanours: Lectures in Honour ...
AbstractWe prove various congruences for Catalan and Motzkin numbers as well as related sequences. T...
AbstractLet b⩾2 be a fixed positive integer and let S(n) be a certain type of binomial sum. In this ...
© Foundation Compositio Mathematica 2004. Cambridge Journals. doi: 10.1112/S0010437X03000022.We give...
AbstractWe prove by the theory of algebraic numbers a result (Theorem 3) which, together with our ea...
Motivated by recently developed interest to the distribution of $q$-arydigits of Mersenne numbers $M...
http://www.math.missouri.edu/~bbanks/papers/index.htmlLet p be a prime and 79 an integer of order t ...
AbstractFor a fixed integer s≥2, we estimate exponential sums with alternative power sums As(n)=∑i=0...
Abstract. Let p be a prime and V an integer of order t in the multiplicative group modulo p. In this...
In this paper, we find all the solutions of the title Diophantine equation in positive integers (m, ...
We show that the equation $\frac{x^p + y^p}{x+y} = p^e z^q$ has no solutions in coprime integers $x,...
AbstractFor a real x ≥ 1 we denote by S[x] the set of squarefull integers n ≤x, that is, the set of ...
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