1 Consider U(15) = {1, 2, 4, 7, 8, 11, 13, 14} under multiplication modulo 15. This group has order 8. To find the order of the element 7, say, we compute the sequence 7^1
In modular arithmetic, the integers coprime (relatively prime) to n from the set
{
0
,
1
,
…
,
n
−
1
}
{\displaystyle \{0,1,\dots ,n-1\}}
of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements of this group can be thought of as the congruence classes, also known as residues modulo n, that are coprime to n.
Hence another name is the group of primitive residue classes modulo n.
In...
it consists of the integers that are relatively prime to $n$