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## Find all generators of Z/(202)

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.4

Find all generators for $\mathbb{Z}/(202)$.

Solution: The generators of $\mathbb{Z}/(202)$ are precisely those (equivalence classes represented by) integers a such that $\mathsf{gcd}(a,202) = 1$. Now 202 factors into primes as $2 \cdot 101$; we eliminate all even numbers between 1 and 202 and 101. So $\mathbb{Z}/(202)$ is generated by all odd$k$, $1 \leq k \leq 202$, with $k \neq 101$.