A reduced residue system modulo " n " can be formed from a complete residue system modulo " n " by removing all integers not relatively prime to " n ".
12.
The reason is that the residue system in reality denotes elements of \ mathbb { Z } / n \ mathbb { Z } and not normal integers, and the concept of " greater than " is not well-defined on such a set.
13.
A complete residue system modulo 10 can be the set { 10, " 9, 2, 13, 24, " 15, 26, 37, 8, 9 } where each integer is in a different congruence class modulo 10.
14.
For example, a complete residue system modulo 12 is { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 } . 1, 5, 7 and 11 are the only integers in this set which are relatively prime to 12, and so the corresponding reduced residue system modulo 12 is { 1, 5, 7, 11 }.
15.
For example, a complete residue system modulo 12 is { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 } . 1, 5, 7 and 11 are the only integers in this set which are relatively prime to 12, and so the corresponding reduced residue system modulo 12 is { 1, 5, 7, 11 }.
