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August 5th, 2017, 04:23 AM   #1
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Help with modules

Please help me prove the following theorem:

This theorem apparently holds when $\displaystyle p$ is prime, and
$\displaystyle a $ is NOT a multiple of $\displaystyle p$.


If,

$\displaystyle ab = ac $ $\displaystyle mod(p)$

Then

$\displaystyle b = c $ $\displaystyle mod(p)$
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August 5th, 2017, 05:04 AM   #2
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When is $a$ invertible? I.e. can you find an $x$ such that $ax=1$ mod(p)?
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August 5th, 2017, 08:52 AM   #3
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The standard notation, for example, $\displaystyle ab \equiv ac \pmod p$, is preferred.
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August 5th, 2017, 04:55 PM   #4
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Quote:
Originally Posted by skipjack View Post
The standard notation, for example, $\displaystyle ab \equiv ac \pmod p$, is preferred.
Not really. Many books have different notations.
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August 5th, 2017, 04:58 PM   #5
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What I meant was "preferred on this website".
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