An almost all result on $q_1 q_2 \equiv c \pmod q$
Abstract
Description
In this paper we consider the congruence equation $q_1 q_2 \equiv c \pmod q$ with $a < q_1 \leq a + q^{1/2+ε}$ and $b < q_2 \leq b + q^{1/2+ε}$ and show that it has solution for almost all $a$ and $b$. Then we apply it to a question of Fujii and Kitaoka as well as generalize it to more variables. At the end, we will present a new way to attack the above congruence equation question through higher moments.
12 pages, the author welcomes any ideas on the higher moment attack
12 pages, the author welcomes any ideas on the higher moment attack