Definition: 7.04: Aliquant Part, a Number Being Not a Divisor of Another Number
But (the lesser number is) parts (of the greater number) when it does not measure it.
This is any integer \(d\neq 0,~|d| < |n|\), which is not a divisor of \(n\). For such integers we write \(d\not\mid n\). These are exactly those integers $d$ which leave a remainder $r$ with $0 < r < |d|$ in the division with quotient and remainder $$n=dq+r,\quad 0 < r < |d|.$$
Proofs: 2 3 4 5 6 7 8 9 10
Propositions: 11 12 13 14 15 16
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016