A generalization of a problem of Chebyshev
A note on the number of -Diophantine quadruples
Let be an -tuple of positive, pairwise distinct integers. If for all the prime divisors of come from the same fixed set , then we call the -tuple -Diophantine. In this note we estimate the number of -Diophantine quadruples in terms of .
A quantitative lower bound for the greatest prime factor of (ab+1)(bc+1)(ca+1)
Almost-primes represented by quadratic polynomials
Arithmetic properties of polynomial specializations over finite fields
Beweis des Satzes, dass jede eigentlich primitive quadratische Form unendlich viele Primzahlen darzustellen fähig ist
Class Number Two for Real Quadratic Fields of Richaud-Degert Type
2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.This paper contains proofs of conjectures made in [16] on class number 2 and what this author has dubbed the Euler-Rabinowitsch polynomial for real quadratic fields. As well, we complete the list of Richaud-Degert types given in [16] and show how the behaviour of the Euler-Rabinowitsch polynomials and certain continued fraction expansions come into play in the complete determination...
Connection between Schinzel’s conjecture and divisibility of the class number
Continued fractions of period five and real quadratic fields of class number one
Criterion for 3 to be eleventh power
Gaussian primes
How many primes can divide the values of a polynomial?
Ještě o kvadratických polynomech nabývajících mnoha prvočíselných hodnot
La conjecture de Dickson et classes particulières d’entiers
En admettant la conjecture de Dickson, nous démontrons que, pour chaque couple d’entiers et , il existe une partie infinie telle que, pour chacun des entiers et tout entier tel que , on ait où sont des nombres premiers. De même, pour chaque couple d’entiers et , il existe une partie infinie telle que, pour chacun des entiers et tout entier (nul ou non ) de l’intervalle , on ait où sont des nombres premiers et l’entier appartient à l’intervalle . La lecture non standard...
Le plus grand facteur premier de n² + 1 où est presque premier
Mémoire sur la composition de polynômes entiers qui n'admettent que des diviseurs premiers d'une forme déterminée
Modifications of the Eratosthenes sieve
We discuss some cancellation algorithms such that the first non-cancelled number is a prime number p or a number of some specific type. We investigate which numbers in the interval (p,2p) are non-cancelled.
New prime-producing quadratic polynomials associated with class number one or two.
On cubic polynomials giving many primes.
On polynomials that are sums of two cubes.
It is proved that, if F(x) be a cubic polynomial with integral coefficients having the property that F(n) is equal to a sum of two positive integral cubes for all sufficiently large integers n, then F(x) is identically the sum of two cubes of linear polynomials with integer coefficients that are positive for sufficiently large x. A similar result is proved in the case where F(n) is merely assumed to be a sum of two integral cubes of either sign. It is deduced that analogous propositions are true...