Proposition: Generating Co-Prime Numbers Knowing the Greatest Common Divisor

If \(d\) is the greatest common divisor of two integers \(a\) and \(b\), then the integers \(\frac ad\) and \(\frac bd\) are co-prime, formally

\[d=\gcd(a,b)\Rightarrow \frac ad\perp \frac bd.\]

Proofs: 1

Proofs: 1 2 3


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References

Bibliography

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