Editing Algebraic number theory (section)

===Dirichlet===
In a couple of papers in 1838 and 1839 [[Peter Gustav Lejeune Dirichlet]] proved the first [[class number formula]], for [[quadratic form]]s (later refined by his student [[Leopold Kronecker]]). The formula, which Jacobi called a result "touching the utmost of human acumen", opened the way for similar results regarding more general [[number field]]s.<ref name=Elstrodt>{{citation | last = Elstrodt | first = Jürgen | journal = Clay Mathematics Proceedings | title = The Life and Work of Gustav Lejeune Dirichlet (1805–1859) | year = 2007 | url = http://www.uni-math.gwdg.de/tschinkel/gauss-dirichlet/elstrodt-new.pdf | access-date = 2007-12-25 | archive-date = 2021-05-22 | archive-url = https://web.archive.org/web/20210522140235/https://www.uni-math.gwdg.de/tschinkel/gauss-dirichlet/elstrodt-new.pdf | url-status = dead }}</ref> Based on his research of the structure of the [[unit group]] of [[quadratic field]]s, he proved the [[Dirichlet unit theorem]], a fundamental result in algebraic number theory.<ref name=Kanemitsu>{{citation | last = Kanemitsu| first = Shigeru|author2=Chaohua Jia| title=Number theoretic methods: future trends | year=2002| publisher=Springer| isbn= 978-1-4020-1080-4| pages= 271–4}}</ref>

He first used the [[pigeonhole principle]], a basic counting argument, in the proof of a theorem in [[diophantine approximation]], later named after him [[Dirichlet's approximation theorem]]. He published important contributions to Fermat's last theorem, for which he proved the cases ''n''&nbsp;=&nbsp;5 and ''n''&nbsp;=&nbsp;14, and to the [[quartic reciprocity|biquadratic reciprocity law]].<ref name=Elstrodt/> The [[Dirichlet divisor problem]], for which he found the first results, is still an unsolved problem in number theory despite later contributions by other researchers.