The reduced residue system modulo $10$ is: $1, 3, 7, 9$
But how could we find these numbers?
The only thing I know is they're relatively prime to $10$.
What does it mean by "no two different elements of the set are congruent to modulo m"?
Thanks,
Chan
Best Answer
The line "no two different elements of the set are congruent modulo $m$" just means that all of your elements are distinct modulo $m$. For example, $1,3,7,9,11,111,1111$ are all relatively prime to $10$, but they do not form a reduced residue system since $1,11,111,1111$ are all the same modulo $10$
Another way to specify the condition is: The reduced residue system modulo $N$ is the set of all integers $m$ with $\gcd(m,N)=1$ and $0\leq m\leq N$.
Hope that helps,