Add to ORKGThis is a preprint of an article published by TÜBİTAK; William D. Banks, Florian Luca, Igor E. Shparlinski, Henning Stichtenoth, “On the value set of n! modulo a prime,” Turkish Journal of Mathematics, 29 (2005), 169-174. Copyright ©2005.We show that for infinitely many prime numbers p there are at least log log p/ log log log p distinct residue classes modulo p that are not congruent to n! for any integer n
AbstractBy some extremely simple arguments, we point out the following:(i)If n is the least positive...
AbstractLet νp denote a totally positive integer of an algebraic number field K such that νp is a le...
AbstractA sequence A = {ai} of positive integers a1 < a2 < ⋯ is said to be primitive if no term of A...
We prove, that the sequence $1!, 2!, 3!, \dots$ produces at least $(\sqrt{2} - o(1))\sqrt{p}$ distin...
We show that for innitely many prime numbers p there are at least log log p = log log log p distinct...
We show that for infinitely many prime numbers p there are at least log log p / log log log p distin...
AbstractWe estimate character sums with Catalan numbers and middle binomial coefficients modulo a pr...
AbstractIn this paper, we prove two results. The first theorem uses a paper of Kim (J. Number Theory...
AbstractIf n is a positive integer, we write n! as a product of n prime powers, each at least as lar...
http://www.math.missouri.edu/~bbanks/papers/index.htmlLet P(n) denote the largest prime factor of an...
AbstractHere, we construct infinitely many number fields of any given degree d>1 whose class numbers...
AbstractWe prove that two sequences arising from two different domains are equal. The first one, {d(...
AbstractIn 1997 Berend proved a conjecture of Erdős and Graham by showing that for every positive in...
AbstractForf(X)∈Z[X], letDf(n) be the least positive integerkfor whichf(1),…,f(n) are distinct modul...
AbstractWe consider, for odd primes p, the function N(p, m, α) which equals the number of subsets S⊆...
AbstractBy some extremely simple arguments, we point out the following:(i)If n is the least positive...
AbstractLet νp denote a totally positive integer of an algebraic number field K such that νp is a le...
AbstractA sequence A = {ai} of positive integers a1 < a2 < ⋯ is said to be primitive if no term of A...
We prove, that the sequence $1!, 2!, 3!, \dots$ produces at least $(\sqrt{2} - o(1))\sqrt{p}$ distin...
We show that for innitely many prime numbers p there are at least log log p = log log log p distinct...
We show that for infinitely many prime numbers p there are at least log log p / log log log p distin...
AbstractWe estimate character sums with Catalan numbers and middle binomial coefficients modulo a pr...
AbstractIn this paper, we prove two results. The first theorem uses a paper of Kim (J. Number Theory...
AbstractIf n is a positive integer, we write n! as a product of n prime powers, each at least as lar...
http://www.math.missouri.edu/~bbanks/papers/index.htmlLet P(n) denote the largest prime factor of an...
AbstractHere, we construct infinitely many number fields of any given degree d>1 whose class numbers...
AbstractWe prove that two sequences arising from two different domains are equal. The first one, {d(...
AbstractIn 1997 Berend proved a conjecture of Erdős and Graham by showing that for every positive in...
AbstractForf(X)∈Z[X], letDf(n) be the least positive integerkfor whichf(1),…,f(n) are distinct modul...
AbstractWe consider, for odd primes p, the function N(p, m, α) which equals the number of subsets S⊆...
AbstractBy some extremely simple arguments, we point out the following:(i)If n is the least positive...
AbstractLet νp denote a totally positive integer of an algebraic number field K such that νp is a le...
AbstractA sequence A = {ai} of positive integers a1 < a2 < ⋯ is said to be primitive if no term of A...