  For a composite $n$ and an odd $c$ with $c$ not dividing $n$, the number of
solutions to the equation $n+a\equiv b\mod c$ with $a,b$ quadratic residues
modulus $c$ is calculated. We establish a direct relation with those modular
solutions and the distances between points of a modular hyperbola. Furthermore,
for certain composite moduli $c$, an asymptotic formula for quotients between
the number of solutions and $c$ is provided. Finally, an algorithm for integer
factorization using such solutions is presented.
