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Proposition: Complete and Reduced Residue Systems (Revised)

Let $a > 0$ and $b > 0$ be positive integers which are co-prime $a\perp b.$ Then the integer $ax+by$ runs through all values of

• a complete residue system modulo $ab,$ if the integers $x$ (respectively $y$) run through all values of the complete residue systems modulo $a$ (respectively $b,$)
• a reduced residue system modulo $ab,$ if the integers $x$ (respectively $y$) run through all values of the reduced residue systems modulo $a$ (respectively $b.$)

Table of Contents

Proofs: 1

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References

Bibliography

1. Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927
2. Jones G., Jones M.: "Elementary Number Theory (Undergraduate Series)", Springer, 1998