> [!NOTE] Definiton (Linear congruence) > A *linear [[Congruence Modulo n|congruence]]* is an equation of the form $ax \equiv b \pmod{n}$where $a,b,$ and $n$ are fixed [[Integers|integers]] or [[Natural Numbers|natural numbers]] and $x$ is a variable ranging over the integers. > >The *solutions* to the congruence are the integers $x$ making the equation hold. # Properties