# if p divides x then is xy(mod p) = 0 ?

• October 10th 2011, 08:09 PM
restin84
if p divides x then is xy(mod p) = 0 ?
I believe I am correct but I am hoping to get some confirmation...

is it true that...

if p|x then xy(mod p) = 0 ?

I need this for a proof and I just want to make sure it is correct before I go any further.
• October 11th 2011, 10:26 AM
roninpro
Re: if p divides x then is xy(mod p) = 0 ?
I think that you can answer your question by answering something more basic: what does it mean to take a number $N$ modulo $p$?
• October 11th 2011, 11:52 AM
Deveno
Re: if p divides x then is xy(mod p) = 0 ?
you may also find it instructive to recall that p|x means x = pk for some integer k, so xy = (pk)y = p(ky),

so (xy) mod p = p(ky) mod p = (p mod p)(ky mod p).