Prove transitivity property of congruence mod m. Show that if $x\equiv y \pmod m$ and $y \equiv z\pmod m$ then $x\equiv z\pmod m$ .
I didn't really get the tutors explanation of this, I get what transitivity is but the congruence mod m confused me… can someone go through it in-depth for me?
Best Answer
$x\equiv y \pmod m$ means that $x-y =km$ for some integer $k$. With the same way we have $y-z=nm$ for an in integer $n$.
Substrat the last from the first to get $x-z=(k-n)m$ which means that $x\equiv z \pmod m$.