On positive integers with a certain nondivisibility property.
On power integral bases for certain pure number fields defined by
Let be a number field generated by a complex root of a monic irreducible polynomial , , is a square free rational integer. We prove that if or and , then the number field is monogenic. If or , then the number field is not monogenic.
On power residue characters of units and the representation of numbers by quadratic forms
On power residues
On power residues
On power series and Mahler's U-numbers.
On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications
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