Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the size of the set A(A+1)   Let $F_p$ be the field of a prime order $p.$ For a subset $A\subset F_p$ we
consider the product set $A(A+1).$ This set is an image of $A\times A$ under
the polynomial mapping $f(x,y)=xy+x:F_p\times F_p\to F_p.$ In the present paper
we show that if $|A|<p^{1/2},$ then $$ |A(A+1)|\ge |A|^{106/105+o(1)}.$$ If
$|A|>p^{2/3},$ then we prove that $$|A(A+1)|\gg \sqrt{p |A|}$$ and show that
this is the optimal in general settings bound up to the implied constant. We
also estimate the cardinality of $A(A+1)$ when $A$ is a subset of real numbers.
We show that in this case one has the Elekes type bound $$ |A(A+1)|\gg
|A|^{5/4}. $$

25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat