On power.free numbers and polynomials. II.
On prime divisors of Mersenne numbers
On prime divisors of remarkable sequences.
On prime factors of integers of the form (ab+1)(bc+1)(ca+1)
1. Introduction. For any integer n > 1 let P(n) denote the greatest prime factor of n. Győry, Sárközy and Stewart [5] conjectured that if a, b and c are pairwise distinct positive integers then (1) P((ab+1)(bc+1)(ca+1)) tends to infinity as max(a,b,c) → ∞. In this paper we confirm this conjecture in the special case when at least one of the numbers a, b, c, a/b, b/c, c/a has bounded prime factors. We prove our result in a quantitative form by showing that if is a finite set of triples (a,b,c)...
On prime factors of sums of integers I
On prime numbers in an arithmetic progression with a prime-power difference
On prime primitive roots
On prime values of reducible quadratic polynomials
It is shown that Dickson’s Conjecture about primes in linear polynomials implies that if f is a reducible quadratic polynomial with integral coefficients and non-zero discriminant then for every r there exists an integer such that the polynomial represents at least r distinct primes.
On primitive divisors of Mersenne numbers
On primitive lattice points in planar domains
On Representing Integers as Products of the p + 1.
On rough and smooth neighbors.
We study the behavior of the arithmetic functions defined byF(n) = P+(n) / P-(n+1) and G(n) = P+(n+1) / P-(n) (n ≥ 1)where P+(k) and P-(k) denote the largest and the smallest prime factors, respectively, of the positive integer k.
On sequences of ±1's defined by binary patterns [Book]
On sets characterizing number-theoretical functions (II) (The set of "prime plus one"'s is a set of quasi-uniqueness)
On sets of weak uniform distribution
On shifted primes
On short sums of certain multiplicative functions.
On Siegel Zeros of Hecke-Landau Zeta-Functions.
On Sieve method and Goldbach problem
On sign-changes in the remainder-term of the prime-number formula, II