Add to ORKGIn the present paper we show that there exist infinitely many consecutive square-free numbers of the form $n^2+1$, $n^2+2$. We also establish an asymptotic formula for the number of such square-free pairs when $n$ does not exceed given sufficiently large positive integer
AbstractLet a1 < a2 < … be a sequence of positive integers such that no ak is a sum of distinct othe...
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number...
AbstractWe solve a problem of Filaseta by proving, that if N is sufficiently large, A ⊆ [N], |A| > N...
In this paper we show that there exist infinitely many square-free numbers of the form $n^2+n+1$. We...
In this note, we prove by using T. Estermann's and S. Dimitrov's arguments with an elementary inequa...
AbstractWe show that the number of subsets of {1,2,…,n} with no solution tox1+x2+…+xk=y1+y2+…+ylfork...
AbstractWe establish an asymptotic formula for the number of positive integers n⩽x for which φ(n) is...
AbstractWe show that for everyk⩾3 the number of subsets of {1, 2, …, n} containing no solution tox1+...
We prove the remaining case of a conjecture of Borwein and Choi concerning an estimate on the square...
We prove that the density of integers ≡2 (mod 24), which can be represented as the sum of two square...
AbstractDenote by A a set of x different natural numbers. The following two results are obtained: 1....
summary:We show that there exist infinitely many consecutive square-free numbers of the form $n^2+1$...
summary:We show that there exist infinitely many consecutive square-free numbers of the form $n^2+1$...
http://www.math.missouri.edu/~bbanks/papers/index.htmlLet '(•) and _(•) denote the Euler function an...
AbstractWe prove that the density of integers ≡2 (mod24), which can be represented as the sum of two...
AbstractLet a1 < a2 < … be a sequence of positive integers such that no ak is a sum of distinct othe...
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number...
AbstractWe solve a problem of Filaseta by proving, that if N is sufficiently large, A ⊆ [N], |A| > N...
In this paper we show that there exist infinitely many square-free numbers of the form $n^2+n+1$. We...
In this note, we prove by using T. Estermann's and S. Dimitrov's arguments with an elementary inequa...
AbstractWe show that the number of subsets of {1,2,…,n} with no solution tox1+x2+…+xk=y1+y2+…+ylfork...
AbstractWe establish an asymptotic formula for the number of positive integers n⩽x for which φ(n) is...
AbstractWe show that for everyk⩾3 the number of subsets of {1, 2, …, n} containing no solution tox1+...
We prove the remaining case of a conjecture of Borwein and Choi concerning an estimate on the square...
We prove that the density of integers ≡2 (mod 24), which can be represented as the sum of two square...
AbstractDenote by A a set of x different natural numbers. The following two results are obtained: 1....
summary:We show that there exist infinitely many consecutive square-free numbers of the form $n^2+1$...
summary:We show that there exist infinitely many consecutive square-free numbers of the form $n^2+1$...
http://www.math.missouri.edu/~bbanks/papers/index.htmlLet '(•) and _(•) denote the Euler function an...
AbstractWe prove that the density of integers ≡2 (mod24), which can be represented as the sum of two...
AbstractLet a1 < a2 < … be a sequence of positive integers such that no ak is a sum of distinct othe...
We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number...
AbstractWe solve a problem of Filaseta by proving, that if N is sufficiently large, A ⊆ [N], |A| > N...