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The set $\{1, 2, 3, \dots , n - 1\}$ is a group under multiplication modulo $n.$ Then the smallest value of $n$ between $20$ and $30$ is $(20, 30$ included $)\;$ _______

We know that the set $\{1, 2, \dots , n - 1\}$ is a group under multiplication modulo $n$ if and only if $n$ is a prime number.

so, the minimum possible value of $n$ between $20$ and $30$ is $23.$

Here i have taken an example and tried to explain how to make it group under multiplication modulo.

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