Definition:Divisor (Algebra)/Integer/Aliquant Part

Definition

An aliquant part of an integer $n$ is a positive integer which is less than $n$ but is not a divisor of $n$.

Also known as

Euclid's term for an aliquant part is parts.

In the words of Euclid:

but parts when it does not measure it.

(The Elements: Book $\text{VII}$: Definition $4$)

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.

Also see

• Definition:Aliquot Part

• Results about aliquant parts can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): aliquant part
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): aliquant part
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): aliquant part