AbstractLet n1 < n2 < … be an infinite sequence of integers. The necessary and sufficient condition that for almost all α the inequality |α − aini| < ϵni2 with (ai, ni) = 1 should have infinitely many solutions is that Σi=1∞ϕ(ni)ni2 = ∞.The techniques used in the proof can perhaps be applied to prove an old conjecture of Duffin and Schaeffer
Let $p$ and $q$ be two distinct fixed prime numbers and $(n_i)_{i\geq 0}$ the sequence of consecutiv...
AbstractAsymptotic results, similar to those of Roth and Szekeres, are obtained for certain partitio...
AbstractThe largest possible number of representations of an integer in thek-fold sumsetkA=A+…+Ais m...
AbstractLet n1 < n2 < … be an infinite sequence of integers. The necessary and sufficient condition ...
AbstractIt is shown that, if ψ(n) is a real function with 0 < ψ(n) < 12, and satisfies a simple regu...
AbstractLet {λi}i = 1s (s ≥ 2) be a finite sequence of non-zero real numbers, not all of the same si...
AbstractThere is no known necessary and sufficient condition on a sequence {αn} of nonnegative real ...
AbstractFor an arbitrary sequence {αn} of nonnegative real numbers there is no known necessary and s...
AbstractA lower bound of Richert on the number of solutions of N − p = P3 is improved
This paper studies the limit behaviour of sums of the form Tn(x)=∑1≤j≤nckj(x),(n=1,2,…)where (cj(x))...
AbstractIn 1966 P. Erdös proved the following theorem:Let B = {bi: 1 < b1 < b2 < b3 < …} be an infin...
AbstractLet ν(n) denote the number of distinct prime factors of n. We show that the equation n + ν(n...
We study the set D of positive integers d for which the equation $\phi(a)-\phi(b)=d$ has infinitely ...
Given two relatively prime positive integers m < n we consider the smallest positive solution (x0, y...
AbstractK. Thanigasalam has shown that for any positive integer k the sequence of positive integers ...
Let $p$ and $q$ be two distinct fixed prime numbers and $(n_i)_{i\geq 0}$ the sequence of consecutiv...
AbstractAsymptotic results, similar to those of Roth and Szekeres, are obtained for certain partitio...
AbstractThe largest possible number of representations of an integer in thek-fold sumsetkA=A+…+Ais m...
AbstractLet n1 < n2 < … be an infinite sequence of integers. The necessary and sufficient condition ...
AbstractIt is shown that, if ψ(n) is a real function with 0 < ψ(n) < 12, and satisfies a simple regu...
AbstractLet {λi}i = 1s (s ≥ 2) be a finite sequence of non-zero real numbers, not all of the same si...
AbstractThere is no known necessary and sufficient condition on a sequence {αn} of nonnegative real ...
AbstractFor an arbitrary sequence {αn} of nonnegative real numbers there is no known necessary and s...
AbstractA lower bound of Richert on the number of solutions of N − p = P3 is improved
This paper studies the limit behaviour of sums of the form Tn(x)=∑1≤j≤nckj(x),(n=1,2,…)where (cj(x))...
AbstractIn 1966 P. Erdös proved the following theorem:Let B = {bi: 1 < b1 < b2 < b3 < …} be an infin...
AbstractLet ν(n) denote the number of distinct prime factors of n. We show that the equation n + ν(n...
We study the set D of positive integers d for which the equation $\phi(a)-\phi(b)=d$ has infinitely ...
Given two relatively prime positive integers m < n we consider the smallest positive solution (x0, y...
AbstractK. Thanigasalam has shown that for any positive integer k the sequence of positive integers ...
Let $p$ and $q$ be two distinct fixed prime numbers and $(n_i)_{i\geq 0}$ the sequence of consecutiv...
AbstractAsymptotic results, similar to those of Roth and Szekeres, are obtained for certain partitio...
AbstractThe largest possible number of representations of an integer in thek-fold sumsetkA=A+…+Ais m...
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