Definition: Co-prime Numbers

The integers \(a,b\) are called co-prime (or relatively prime), if their greates common divisor i\(\gcd(a,b)=1\), i.e. if \(1\) is the only positive common divisor is equal $1$, i.e. $\gcd(a,b)=1.$

Coprimality is a relation "$\perp$" defined on the set of integers $\perp\subseteq\mathbb Z\times\mathbb Z$ by \[a\perp b:\Leftrightarrow\gcd(a,b)=1.\]

  1. Proposition: Generating Co-Prime Numbers Knowing the Greatest Common Divisor
  2. Proposition: Generating the Greatest Common Divisor Knowing Co-Prime Numbers
  3. Proposition: Divisors of a Product Of Two Factors, Co-Prime to One Factor Divide the Other Factor

Algorithms: 1
Corollaries: 2
Definitions: 3 4 5 6 7 8
Examples: 9
Lemmas: 10 11
Proofs: 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Propositions: 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
Sections: 53
Solutions: 54
Theorems: 55 56 57


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References

Bibliography

  1. Landau, Edmund: "Vorlesungen ├╝ber Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927