$-3 \equiv 17$
Find the mod number.
Ex: $-3 \equiv 17 ~~{\rm(mod~5)}$
How would I find the mod number?
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2Do you mean, "How would I find the numbers $m$ such that $-3\equiv 17\bmod m$"? – Zev Chonoles Jun 02 '13 at 03:38
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I take it you are told that $$-3\equiv 17\pmod{m}$$ and you want $m$.
The above congruence says that $m$ divides $17-(-3)$. So the possible $m$ are all the divisors of $20$. As you mentioned, $5$ is one of them.
André Nicolas
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$a$ is a divisor (factor) of $b$ if there is an integer $q$ such that $aq=b$. It is a matter of taste whether we restrict to positive integers or not. So the positive divisors of $20$ are $1,2,4,5,10,20$. – André Nicolas Jun 02 '13 at 17:06
