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Find $a$ inverse modulo 30, $1\le a \le 30$. For each a you find, find the inverse of each a that have inverse modulo 30

a={1,7,11,13,17,19,23,29}

They got a by the fact that relative primes are inverses. I was wondering if this rule also applied if $a \ge 30$?

Find the inverse of each of the integers in a that have an inverse modulo 30

Not really sure how to do this part

Gooby
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  • "which is essentially all primes" Look at this again. $3$ is not relatively prime to $30$. Neither is $5$. On the other hand, $7$ is relatively prime to $30$. – JMoravitz Oct 17 '19 at 19:58
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    I don't understand what you are asking, but note that $7\times13\equiv1\pmod{30}$. – Angina Seng Oct 17 '19 at 19:59
  • This is not clear. $13\times 7 \equiv 1 \pmod {30}$ since $13\times 7=91\equiv 1 \pmod {30}$. Thus the inverse of $7\pmod {30}$ is $13$. – lulu Oct 17 '19 at 19:59
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    As for how to find the inverses... one suggested search term you can use is "Extended Euclidean Division Algorithm" – JMoravitz Oct 17 '19 at 20:00
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    "I was under the impression that relative prime mean $ax\equiv 1\pmod{30}$" Relatively prime is usually defined as meaning $a$ is relatively prime to $b$ iff $\gcd(a,b)=1$. You can find other equivalent conditions to this of course, but that is the one you should be leaning towards first. – JMoravitz Oct 17 '19 at 20:02
  • How does extended Euclidean division algorithm help? – Gooby Oct 17 '19 at 20:18

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