Proposition: Greatest Common Divisors Of Integers and Prime Numbers

Let \(a\) be an integer and let \(p\) be a prime number. Then, the greatest common divisor of \(p\) and \(a\) is either \(p\) (if \(p\) divides \(a\)), or \(1\) else. Formally,

\[\gcd(p,a)=\cases{p,&\text{if }p\mid a\\1,&\text{if }p\not\mid a}\]

Proofs: 1


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References

Bibliography

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