# A Simpler Dense Proof Regarding the Abundancy Index

@article{Ryan2003ASD,
title={A Simpler Dense Proof Regarding the Abundancy Index},
author={Richard F. Ryan},
journal={Mathematics Magazine},
year={2003},
volume={76},
pages={299 - 301}
}
• R. F. Ryan
• Published 1 October 2003
• Philosophy, Economics
• Mathematics Magazine
(B) If I (a) = r/s is in lowest terms, then s divides a. This follows since sa (a) = ra and gcd(r, s) = 1. (C) If I (a) = r/s is in lowest terms then r > ar(s). This follows from properties (B) and (A) since r/s = I (a) > I (s) = a(s)/s. (The condition that r and s be relatively prime is an important one! Note that 1(2) = 6/4 even though 6 r then r/s is not an abundancy index.
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