On power series with only finitely many coefficients(mod 1): Solution of a problem of Pisot and Salem
On power values of pyramidal numbers, I
On power-free numbers and polynomials. I.
On power.free numbers and polynomials. II.
On powerful numbers.
On powers of 2 dividing the values of certain plane partition functions.
On powers of the theta-function greater than the eighth
On practical partitions.
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 factors of sums of integers III
On prime numbers in an arithmetic progression with a prime-power difference
On prime numbers p,q and r such that pq, pr, and qr are pseudoprimes
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 prime-detecting sequences from Apéry's recurrence formulae for and .
On primitive 3-smooth partitions of .
On primitive divisors of Mersenne numbers