We discuss possible generalizations of Erdŏs\u27s problem about factorials in Fp to the Artin-Schreier extension Fpp of Fp. The generalizations are related to Bell numbers in Fp and to Kurepa\u27s conjecture
Ahlswede R, Khachatrian LH. On extremal sets without coprimes. Acta Arithmetica. 1994;66(1):89-90
We prove that there exist infinitely many coprime numbers $a$, $b$, $c$ with $a+b=c$ and $c>\operato...
AbstractLet r = pλ, K = Fr(t), f be an irreducible monic polynomial in Fr[t], K(Λf) the cyclotomic f...
We prove under a mild condition that Kurepa's conjecture holds for the set of prime numbers \(p\) su...
We prove, that the sequence $1!, 2!, 3!, \dots$ produces at least $(\sqrt{2} - o(1))\sqrt{p}$ distin...
AbstractWe study properties of the polynomials φk(X) which appear in the formal development Πk − 0n ...
In 1927, Emil Artin conjectured a product expression for the density of primes p for which a given ...
AbstractLet p ≥ 5 be a prime and a, b, c relatively prime integers such that ap + bp + cp = 0. A the...
The left factorial of n is defined to be 0! + 1! + ··· + (n − 1)! and is denoted by !n. Kurepa conje...
Let ( {F_n}_{ngeq 0} ) be the sequence of Fibonacci numbers and let (p) be a prime. For an integer (...
AbstractIn 1997 Berend proved a conjecture of Erdős and Graham by showing that for every positive in...
AbstractWe show that for A ranging over n×n circulants with three ones in each row, where n is prime...
In this article, we study the Euler's factorial series $F_p(t)=\sum_{n=0}^\infty n!t^n$ in $p$-adic ...
AbstractWe consider some implications of the generalized Riemann hypothesis using Ihara's zeta funct...
Version V2 contains cosmetic changes and a modification of the definition of $r$-admissibility.Inter...
Ahlswede R, Khachatrian LH. On extremal sets without coprimes. Acta Arithmetica. 1994;66(1):89-90
We prove that there exist infinitely many coprime numbers $a$, $b$, $c$ with $a+b=c$ and $c>\operato...
AbstractLet r = pλ, K = Fr(t), f be an irreducible monic polynomial in Fr[t], K(Λf) the cyclotomic f...
We prove under a mild condition that Kurepa's conjecture holds for the set of prime numbers \(p\) su...
We prove, that the sequence $1!, 2!, 3!, \dots$ produces at least $(\sqrt{2} - o(1))\sqrt{p}$ distin...
AbstractWe study properties of the polynomials φk(X) which appear in the formal development Πk − 0n ...
In 1927, Emil Artin conjectured a product expression for the density of primes p for which a given ...
AbstractLet p ≥ 5 be a prime and a, b, c relatively prime integers such that ap + bp + cp = 0. A the...
The left factorial of n is defined to be 0! + 1! + ··· + (n − 1)! and is denoted by !n. Kurepa conje...
Let ( {F_n}_{ngeq 0} ) be the sequence of Fibonacci numbers and let (p) be a prime. For an integer (...
AbstractIn 1997 Berend proved a conjecture of Erdős and Graham by showing that for every positive in...
AbstractWe show that for A ranging over n×n circulants with three ones in each row, where n is prime...
In this article, we study the Euler's factorial series $F_p(t)=\sum_{n=0}^\infty n!t^n$ in $p$-adic ...
AbstractWe consider some implications of the generalized Riemann hypothesis using Ihara's zeta funct...
Version V2 contains cosmetic changes and a modification of the definition of $r$-admissibility.Inter...
Ahlswede R, Khachatrian LH. On extremal sets without coprimes. Acta Arithmetica. 1994;66(1):89-90
We prove that there exist infinitely many coprime numbers $a$, $b$, $c$ with $a+b=c$ and $c>\operato...
AbstractLet r = pλ, K = Fr(t), f be an irreducible monic polynomial in Fr[t], K(Λf) the cyclotomic f...
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