Problem - 02 - National Math Camp 2021 Number Theory Exam - "Group theory"
- Anindya Biswas
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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."
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Re: Problem - 02 - National Math Camp 2021 Number Theory Exam - "Group theory"
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.
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Re: Problem - 02 - National Math Camp 2021 Number Theory Exam - "Group theory"
ig it may have something to do with primitive roots