1 answer

From A First Course In Number Theory. Note, we are looking for a lot of detail....

Question:

3. A collection of n integers an, ..., An is said to form a complete set of residues (or complete system of residues) modulo

From A First Course In Number Theory.
Note, we are looking for a lot of detail. Please don't leave out any steps.

3. A collection of n integers an, ..., An is said to form a complete set of residues (or complete system of residues) modulo n if every integer is congruent modulo n to one and only one of ak (or, equivalently, a1,..., an are congruent modulo n to 0,1,2,...,n - 1). Prove the following statement: If an,..., an is a complete set of residues modulo n and gcd(a, n) = 1, then aan,..., aan is also a complete set of residues modulo n.

Answers

m. T We first prove the following lemma : Temma . A set of m incongruent integers modulo - m forms a complete residue system

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