# very quick modulo question

• Dec 3rd 2009, 07:06 AM
sirellwood
very quick modulo question
What is 10 x -38 mod 11?

What is 16 x -80 mod 16?

What is 278-421 mod 19?
• Dec 3rd 2009, 07:47 AM
Bruno J.
$\displaystyle 10\times -38 \equiv -1 \times -38 \equiv 5 \mod 11$

$\displaystyle 16\times -80 \equiv 0 \times -80 \equiv 0 \mod 16$

$\displaystyle 278\times -421 \equiv 12 \times -3 \equiv 17 \mod 19$
• Dec 3rd 2009, 08:10 AM
sirellwood
Thanks

I got 9 for the 3rd one....
• Dec 3rd 2009, 02:34 PM
Bacterius
No it is indeed $\displaystyle 17$ for the last one, because $\displaystyle 278 \equiv 12 \ \ \ \ [19]$ and $\displaystyle -421 \equiv -3 \ \ \ \ [19]$.

EDIT : ah yes chiph588@ you are right, but why put a substraction question following two multiplication questions ? This is confusing (Nod)
• Dec 3rd 2009, 03:52 PM
chiph588@
For the third are you wanting $\displaystyle 278\cdot(-421) \mod{19}$ or $\displaystyle (278-421) \mod{19}$?

If it is the latter, then $\displaystyle 9$ is the correct answer.