Definition:Divisor (Algebra)/Integer/Aliquot Part
Jump to navigation
Jump to search
Definition
An aliquot part of an integer $n$ is a divisor of $n$ which is strictly less than $n$.
Also known as
Euclid's term for an aliquot part is just part.
In the words of Euclid:
(The Elements: Book $\text{VII}$: Definition $3$)
Referring to aliquot part and aliquant part as part and parts respectively can be the source of considerable confusion when it is necessary to refer to the plural forms of either term.
Hence the use of part or parts for these concepts is heavily deprecated.
For historical reasons, and historical reasons only, the terms part and parts have been retained in the material quoted directly from Euclid's The Elements.
Some sources give the term as aliquot divisor.
Also see
Linguistic Note
The word aliquot is a Latin word meaning a few, some, or not many.
Sources
- 1919: Leonard Eugene Dickson: History of the Theory of Numbers: Volume $\text { I }$ ... (previous) ... (next): Preface
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): aliquot part
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): aliquot part
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): aliquot part
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): aliquot part
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): aliquot part