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 \[a|a_n.\]

Proofs: 1

Thank you to the contributors under CC BY-SA 4.0!




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