1. ## mods

623x is congruent to 4(mod 679)?

2. Originally Posted by meshel88
623x is congruent to 4(mod 679)?

This equation has no solution since $623x=4\!\!\!\pmod{679}\Longrightarrow 623x\cdot 4^{-1}=1\!\!\!\pmod{679}$ (why does $4^{-1}\!\!\!\pmod{679}$ exist?) $\Longrightarrow 623$ is a unit modulo $679 \Longleftrightarrow 623$ is a unit

in $\mathbb{Z}_{679}$ , which is absurd as $623\,,\,\,679$ are NOT coprime, as you can easily check.

Tonio