Problem - 02 - National Math Camp 2021 Number Theory Exam - "Group theory"

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Anindya Biswas
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Problem - 02 - National Math Camp 2021 Number Theory Exam - "Group theory"

Unread post by Anindya Biswas » Thu May 06, 2021 4:27 pm

Let $p$ be a prime number. We call a subset $S$ of $\{1,2,\cdots,p-1\}$ "good" if it satisfies the property that for every $x,y\in S, xy\text{ mod }{p}$ is also in $S$. How many "good" sets are there?
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
John von Neumann

Naeem Mashkur
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Re: Problem - 02 - National Math Camp 2021 Number Theory Exam - "Group theory"

Unread post by Naeem Mashkur » Wed Jun 16, 2021 9:28 am

Notice that p is congruent to a modulo b, Where 'a' belongs to {1,2,3....,p-1} and b is any positive integer. Also notice that those integer{1,2,3....p-1} are situated in subset S. So, we must find a subset S for every p.

Nayer_Sharar
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Re: Problem - 02 - National Math Camp 2021 Number Theory Exam - "Group theory"

Unread post by Nayer_Sharar » Thu Jun 17, 2021 8:11 pm

ig it may have something to do with primitive roots

Zeta
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Re: Problem - 02 - National Math Camp 2021 Number Theory Exam - "Group theory"

Unread post by Zeta » Sat Mar 19, 2022 3:07 pm

It's graph theory.

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