**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

\[a\perp b:\Leftrightarrow\gcd(a,b)=1.\]

| | | | | created: 2019-03-10 19:28:25 | modified: 2019-03-10 19:33:59 | by: *bookofproofs* | references: [1272]

## 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

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[1272] **Landau, Edmund**: “Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927

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