Quick Modular Property Help

Question

Is this property always true?

if $x \mod y = z$, then $ax \mod ay = az$?

for all intergers $x,y,z,a$.

Is "mod" an operator, so $\ x\ {\rm mod}\ y\ $ denotes the remainder, or is "mod" a relation, denoting congruence, i.e. $,x\equiv y\pmod z \iff z\mid x-y\ ?$ — Bill Dubuque, Apr 25 '14 at 21:21

score 1 · Accepted Answer · answered Apr 25 '14 at 19:31

1

Yes, $x \equiv z \pmod y \implies x = yk+z$. Then $ax = ayk+za$ and the conclusion follows.

answered Apr 25 '14 at 19:31

Sandeep Silwal

It's not true if mod denotes a operator (as written). – Bill Dubuque Apr 25 '14 at 21:29

1 Answers1