Editing Chinese remainder theorem (section)

==History==
The earliest known statement of the problem appears in the 5th-century book ''[[Sunzi Suanjing]]'' by the Chinese mathematician Sunzi:<ref name=Katz>{{harvnb|Katz|1998|page=197}}</ref>

{{blockquote|There are certain things whose number is unknown. If we count them by threes, we have two left over; by fives, we have three left over; and by sevens, two are left over. How many things are there?<ref>{{harvnb|Dence|Dence|1999|page=156}}</ref>}}

Sunzi's work would not be considered a [[theorem]] by modern standards; it only gives one particular problem, without showing how to solve it, much less any [[mathematical proof|proof]] about the general case or a general [[algorithm]] for solving it.<ref>{{harvnb|Dauben|2007|page=302}}</ref> An algorithm for solving this problem was described by [[Aryabhata]] (6th century).<ref>{{harvnb|Kak|1986}}</ref> Special cases of the Chinese remainder theorem were also known to [[Brahmagupta]] (7th century) and appear in [[Fibonacci]]'s [[Liber Abaci]] (1202).<ref>{{harvnb|Pisano|2002|pages=402–403}}</ref> The result was later generalized with a complete solution called ''Da-yan-shu'' ({{lang|zh|大衍術}}) in [[Qin Jiushao]]'s 1247 ''[[Mathematical Treatise in Nine Sections]]'' <ref>{{harvnb|Dauben|2007|page=310}}</ref> which was translated into English in early 19th century by British missionary [[Alexander Wylie (missionary)|Alexander Wylie]].<ref>{{harvnb|Libbrecht|1973}}</ref>

[[File:Disqvisitiones-800.jpg|thumb|The Chinese remainder theorem appears in [[Carl Friedrich Gauss|Gauss]]'s 1801 book ''[[Disquisitiones Arithmeticae]]''.<ref name="Gauss1801.loc=32-36">{{Harvnb|Gauss|1986|loc=Art. 32–36}}</ref>]]

The notion of congruences was first introduced and used by [[Carl Friedrich Gauss]] in his ''[[Disquisitiones Arithmeticae]]'' of 1801.<ref>{{harvnb|Ireland|Rosen|1990|page=36}}</ref> Gauss illustrates the Chinese remainder theorem on a problem involving calendars, namely, "to find the years that have a certain period number with respect to the solar and lunar cycle and the Roman indiction."<ref>{{harvnb|Ore|1988|page=247}}</ref> Gauss introduces a procedure for solving the problem that had already been used by [[Leonhard Euler]] but was in fact an ancient method that had appeared several times.<ref>{{harvnb|Ore|1988|page=245}}</ref>