# very quick modulo question

• December 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?
• December 3rd 2009, 07:47 AM
Bruno J.
$10\times -38 \equiv -1 \times -38 \equiv 5 \mod 11$

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

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

No it is indeed $17$ for the last one, because $278 \equiv 12 \ \ \ \ [19]$ and $-421 \equiv -3 \ \ \ \ [19]$.
For the third are you wanting $278\cdot(-421) \mod{19}$ or $(278-421) \mod{19}$?
If it is the latter, then $9$ is the correct answer.