AbstractLet {λi}i = 1s (s ≥ 2) be a finite sequence of non-zero real numbers, not all of the same sign and in which not all the ratios λiλj are rational. A given sequence of positive integers {ni}i = 1s is said to have property (P) ((P∗) respectively) if for any {λi}i = 1s and any real number η, there exists a positive constant σ, depending on {λi}i = 1s and {ni}i = 1s only, so that the inequality |η + Σi = 1s λixini| < (max xi)−σ has infinitely many solutions in positive integers (primes respectively) x1, x2,…, xs. In this paper, we prove the following result: Given a sequence of positive integers {ni}i = 1∞, a necessary and sufficient condition that, for any positive integer j, there exists an integer s, depending on {ni}i = j∞ only, such...
Let b=((24!)!)!, and let P_{n^2+1} denote the set of all primes of the form n^2+1. Let M denote the ...
AbstractIn 1966 P. Erdös proved the following theorem:Let B = {bi: 1 < b1 < b2 < b3 < …} be an infin...
AbstractWe construct infinite sequences of non-trivial families for which the following three inequa...
AbstractLet {λi}i = 1s (s ≥ 2) be a finite sequence of non-zero real numbers, not all of the same si...
AbstractIt is shown that if λ1, …, λ5 are non-zero real numbers, not all of the same sign, and at le...
AbstractLet n1 < n2 < … be an infinite sequence of integers. The necessary and sufficient condition ...
AbstractIt is shown that λ1, λ2,…, λ6, μ are not all of the same sign and at least one ratio λiλj is...
AbstractLet A, B, G0, G1 be integers, and Gn = AGn − 1 − BGn − 2 for n ≥ 2. Let further S be the set...
AbstractIt is shown that if λ1,…, λ6 are nonzero real numbers, not all of the same sign, such that λ...
AbstractIt is shown that, if ψ(n) is a real function with 0 < ψ(n) < 12, and satisfies a simple regu...
AbstractA lower bound of Richert on the number of solutions of N − p = P3 is improved
AbstractFor an arbitrary sequence {αn} of nonnegative real numbers there is no known necessary and s...
AbstractThere is no known necessary and sufficient condition on a sequence {αn} of nonnegative real ...
AbstractLet a, b, k be non-zero integers. Then the set of pairs of exponents (m, n), m ≧ 1, n ≧ 1, f...
This is the definitive version to appear in Journal de Théorie des Nombres de Bordeaux: 12 pages, no...
Let b=((24!)!)!, and let P_{n^2+1} denote the set of all primes of the form n^2+1. Let M denote the ...
AbstractIn 1966 P. Erdös proved the following theorem:Let B = {bi: 1 < b1 < b2 < b3 < …} be an infin...
AbstractWe construct infinite sequences of non-trivial families for which the following three inequa...
AbstractLet {λi}i = 1s (s ≥ 2) be a finite sequence of non-zero real numbers, not all of the same si...
AbstractIt is shown that if λ1, …, λ5 are non-zero real numbers, not all of the same sign, and at le...
AbstractLet n1 < n2 < … be an infinite sequence of integers. The necessary and sufficient condition ...
AbstractIt is shown that λ1, λ2,…, λ6, μ are not all of the same sign and at least one ratio λiλj is...
AbstractLet A, B, G0, G1 be integers, and Gn = AGn − 1 − BGn − 2 for n ≥ 2. Let further S be the set...
AbstractIt is shown that if λ1,…, λ6 are nonzero real numbers, not all of the same sign, such that λ...
AbstractIt is shown that, if ψ(n) is a real function with 0 < ψ(n) < 12, and satisfies a simple regu...
AbstractA lower bound of Richert on the number of solutions of N − p = P3 is improved
AbstractFor an arbitrary sequence {αn} of nonnegative real numbers there is no known necessary and s...
AbstractThere is no known necessary and sufficient condition on a sequence {αn} of nonnegative real ...
AbstractLet a, b, k be non-zero integers. Then the set of pairs of exponents (m, n), m ≧ 1, n ≧ 1, f...
This is the definitive version to appear in Journal de Théorie des Nombres de Bordeaux: 12 pages, no...
Let b=((24!)!)!, and let P_{n^2+1} denote the set of all primes of the form n^2+1. Let M denote the ...
AbstractIn 1966 P. Erdös proved the following theorem:Let B = {bi: 1 < b1 < b2 < b3 < …} be an infin...
AbstractWe construct infinite sequences of non-trivial families for which the following three inequa...