Proof

(related to Proposition: Sign of Divisors of Integers)

\[\begin{array}{rcl} -b=(-q)a&\Longrightarrow&a\mid-b\\ b=(-q)(-a)&\Longrightarrow&-a\mid b\\ -b=q(-a)&\Longrightarrow&-a\mid-b\\ |b|=|q||a|&\Longrightarrow&|a|~\mid~|b|\\ \end{array} \]


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References

Bibliography

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