very quick modulo question

**sirellwood** · December 3rd 2009, 07:06 AM

What is 10 x -38 mod 11?

What is 16 x -80 mod 16?

What is 278-421 mod 19?

**Bruno J.** · December 3rd 2009, 07:47 AM

$10\times -38 \equiv -1 \times -38 \equiv 5 \mod 11$

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

$278\times -421 \equiv 12 \times -3 \equiv 17 \mod 19$

**sirellwood** · December 3rd 2009, 08:10 AM

Thanks

Shouldnt i get numerical answers?

I got 9 for the 3rd one....

**Bacterius** · December 3rd 2009, 02:34 PM

No it is indeed $17$ for the last one, because $278 \equiv 12 \ \ \ \ [19]$ and $-421 \equiv -3 \ \ \ \ [19]$ .

EDIT : ah yes chiph588@ you are right, but why put a substraction question following two multiplication questions ? This is confusing

**chiph588@** · December 3rd 2009, 03:52 PM

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.

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