For nonempty sets $A,B$ of nonnegative integers and an integer $n$, let $r_{A,B}(n)$ be the number of representations of $n$ as $a+b$ and $d_{A,B}(n)$ be the number of representations of $n$ as $a-b$, where $a\in A, b\in B$. In this paper, we determine the sets $A,B$ such that $r_{A,B}(n)=1$ for every nonnegative integer $n$. We also consider the \emph{difference} structure and prove that: there exist sets $A$ and $B$ of nonnegative integers such that $r_{A,B}(n)\ge 1$ for all large $n$, $A(x)B(x)=(1+o(1))x$ and for any given nonnegative integer $c$, we have $d_{A,B}(n)=c$ for infinitely many positive integers $n$. Other related results are also contained.Comment: 7 page
Let $\beta > 1$ be a real number, and let $\{ a_k\}$ be an unbounded sequence of positive integers s...
Let $\beta > 1$ be a real number, and let $\{ a_k\}$ be an unbounded sequence of positive integers s...
For a given set A of nonnegative integers the representation functions R2(A, n), R3(A, n) are define...
summary:Let $n > m \geq 2$ be positive integers and $n=(m+1) \ell +r$, where $0 \leq r \leq m.$ Let ...
summary:Let $n > m \geq 2$ be positive integers and $n=(m+1) \ell +r$, where $0 \leq r \leq m.$ Let ...
AbstractLet A be a set of nonnegative integers. For h≥2, denote by hA the set of all the integers re...
summary:Let $n > m \geq 2$ be positive integers and $n=(m+1) \ell +r$, where $0 \leq r \leq m.$ Let ...
For a set of nonnegative integers S let RS(n) denote the number of unordered representations of the ...
Abstract. We present a versatile construction allowing one to obtain pairs of integer sets with infi...
Abstract. We prove that there exists an absolute constant c> 0 such that for any finite set A ⊆ Z...
Let b ≥ 2 be a fixed integer. Let sb(n) denote the sum of digits of the nonnegative integer n in the...
Let $d \geq 4$ be a natural number and let $A$ be a finite, non-empty subset of $\mathbb{R}^d$ such ...
Let $\beta > 1$ be a real number, and let $\{ a_k\}$ be an unbounded sequence of positive integers s...
Let $\beta > 1$ be a real number, and let $\{ a_k\}$ be an unbounded sequence of positive integers s...
Let $\beta > 1$ be a real number, and let $\{ a_k\}$ be an unbounded sequence of positive integers s...
Let $\beta > 1$ be a real number, and let $\{ a_k\}$ be an unbounded sequence of positive integers s...
Let $\beta > 1$ be a real number, and let $\{ a_k\}$ be an unbounded sequence of positive integers s...
For a given set A of nonnegative integers the representation functions R2(A, n), R3(A, n) are define...
summary:Let $n > m \geq 2$ be positive integers and $n=(m+1) \ell +r$, where $0 \leq r \leq m.$ Let ...
summary:Let $n > m \geq 2$ be positive integers and $n=(m+1) \ell +r$, where $0 \leq r \leq m.$ Let ...
AbstractLet A be a set of nonnegative integers. For h≥2, denote by hA the set of all the integers re...
summary:Let $n > m \geq 2$ be positive integers and $n=(m+1) \ell +r$, where $0 \leq r \leq m.$ Let ...
For a set of nonnegative integers S let RS(n) denote the number of unordered representations of the ...
Abstract. We present a versatile construction allowing one to obtain pairs of integer sets with infi...
Abstract. We prove that there exists an absolute constant c> 0 such that for any finite set A ⊆ Z...
Let b ≥ 2 be a fixed integer. Let sb(n) denote the sum of digits of the nonnegative integer n in the...
Let $d \geq 4$ be a natural number and let $A$ be a finite, non-empty subset of $\mathbb{R}^d$ such ...
Let $\beta > 1$ be a real number, and let $\{ a_k\}$ be an unbounded sequence of positive integers s...
Let $\beta > 1$ be a real number, and let $\{ a_k\}$ be an unbounded sequence of positive integers s...
Let $\beta > 1$ be a real number, and let $\{ a_k\}$ be an unbounded sequence of positive integers s...
Let $\beta > 1$ be a real number, and let $\{ a_k\}$ be an unbounded sequence of positive integers s...
Let $\beta > 1$ be a real number, and let $\{ a_k\}$ be an unbounded sequence of positive integers s...
For a given set A of nonnegative integers the representation functions R2(A, n), R3(A, n) are define...