◀ ▲ ▶Branches / Number-theory / Corollary: Divisors of a Product Of Many Factors, Co-Prime to All But One Factor, Divide This Factor
Corollary: Divisors of a Product Of Many Factors, Co-Prime to All But One Factor, Divide This Factor
(related to Proposition: Divisors of a Product Of Two Factors, Co-Prime to One Factor Divide the Other Factor)
This is a generalization of the corresponding theorem for two factors. If \[a|\prod_{\nu=1}^n a_\nu,\quad n\ge 2\]
and if \[a\perp a_\nu,\quad 1\le \nu < n,\]
then
\[a|a_n.\]
Table of Contents
Proofs: 1
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References
Bibliography
- Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927
