Help me understand the definition of complete residue system.
Definition: The set of integers {r1, r2, ..., rs} is called a complete residue system if:
i) r_i not congruent to r_j whenever i ≠ j;
ii) for each integer n, there corresponds an r_i such that n ≡ r_i (mod m).
Is the set {1,2,3} a complete residue system mod 3?

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I think condition (i) is easy to check. Having difficult time with condition (ii)

Condition ii just says, you need \(n\) integers to form a complete residue set in modulus \(n\)

so if we have modulo 6 would the complete residue be [0,1,2,3,4,5] ?

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