Proof: By Euclid

(related to Corollary: 7.02: Any Divisor Dividing Two Numbers Divides Their Greatest Common Divisor)

If \(\gcd(a,b\)) is the greatest common divisor of \(a\) and \(b\), then it is, by definition, the maximum of all possible common divisors $d\mid a\wedge d\mid b.$


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References

Bibliography

  1. Scheid Harald: "Zahlentheorie", Spektrum Akademischer Verlag, 2003, 3rd Edition