Abstract
AbstractFor a set A of positive integers and any positive integer n, let
$R_{1}(A, n)$
,
$R_{2}(A,n)$
and
$R_{3}(A,n)$
denote the number of solutions of
$a+a^{\prime }=n$
with
$a, a^{\prime }\in A$
and the additional restriction that
$a<a^{\prime }$
for
$R_{2}$
and
$a\leq a^{\prime }$
for
$R_{3}$
. We consider Problem 6 of Erdős et al. [‘On additive properties of general sequences’, Discrete Math.136 (1994), 75–99] about locally small and locally large values of
$R_{1}, R_{2}$
and
$R_{3}$
.
Publisher
Cambridge University Press (CUP)