Editing Modulo (mathematics) (section)

==History==
''Modulo'' is a [[mathematical jargon]] that was introduced into [[mathematics]] in the book ''[[Disquisitiones Arithmeticae]]'' by [[Carl Friedrich Gauss]] in 1801.<ref>{{Cite journal|last=Bullynck|first=Maarten|date=2009-02-01|title=Modular arithmetic before C.F. Gauss: Systematizations and discussions on remainder problems in 18th-century Germany|journal=Historia Mathematica|volume=36|issue=1|pages=48–72|doi=10.1016/j.hm.2008.08.009|issn=0315-0860|doi-access=}}</ref>  Given the [[integer]]s ''a'', ''b'' and ''n'', the expression "''a'' ≡ ''b'' (mod ''n'')", pronounced "''a'' is congruent to ''b'' modulo ''n''", means that ''a''&nbsp;−&nbsp;''b'' is an integer multiple of ''n'', or equivalently, ''a'' and ''b'' both share the same remainder when divided by ''n''. It is the [[Latin]] [[ablative]] of ''[[wikt:modulus|modulus]]'', which itself means "a small measure."<ref>{{Citation|title=modulo|url=https://www.thefreedictionary.com/modulo|work=The Free Dictionary|access-date=2019-11-21}}</ref> 

The term has gained many meanings over the years—some exact and some imprecise. The most general precise definition is simply in terms of an [[equivalence relation]] ''R'', where ''a'' is ''equivalent'' (or ''congruent)'' to ''b'' modulo ''R'' if ''aRb''.