Proposition: Sign of Divisors of Integers

Let \(a,b\in\mathbb Z\) and let \(a\) be a divisor of \(b\). From the divisibility \(a\mid b\) the following divisibility relations follow: \(a\mid -b~\), \(~-a\mid b~\),\(~-a\mid -b\) and \(|a|~\mid ~|b|\).

Proofs: 1

Explanations: 1
Proofs: 2 3
Propositions: 4


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References

Bibliography

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