◀ ▲ ▶Branches / Number-theory / Proposition: Generating the Greatest Common Divisor Knowing Co-Prime Numbers
Proposition: Generating the Greatest Common Divisor Knowing Co-Prime Numbers
If \(c > 0\) is a common divisor of two integers \(a\) and \(b\), and if the integers $\frac ac$ and \(\frac bc\) are co-prime, then \(c\) is the greatest common divisor of \(a\) and \(b\), formally
\[c > 0\wedge c\mid a\wedge c\mid b\wedge \frac ac\perp \frac bc\Rightarrow c=\gcd(a,b).\]
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1
Thank you to the contributors under CC BY-SA 4.0! 
- Github:
-
References
Bibliography
- Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927
