"2000 (عدد)" کے نسخوں کے درمیان فرق

* '''2328 (عدد)''' – sum of the totient function for the first 87 integers, the number of groups of order 128, see [http://www-public.tu-bs.de:8080/~beick/soft/small/small.html] {{wayback|url=http://www-public.tu-bs.de:8080/~beick/soft/small/small.html |date=20070204070922 }}.

* '''{{Vanchor|2719}}''' – largest known odd number which cannot be expressed in the form [[Ramanujan's ternary quadratic form|''x''² + ''y''² + 10''z''²]] where ''x'', ''y'' and ''z'' are integers.<ref>{{cite web|title=Odd numbers that are not of the form x^2+y^2+10*z^2.|url=http://oeis.org/search?q=3,+7,+21,+31,+33,+43,&language=english&go=Search|work=The Online Encyclopedia of Integer Sequences|publisher=The OEIS Foundation, Inc.|accessdate=13 November 2012}}</ref> In 1997 it was conjectured that this is also the largest such odd number.<ref name=Ono>{{cite journal|last=Ono|first=Ken|title=Ramanujan, taxicabs, birthdates, zipcodes and twists|journal=American Mathematical Monthly|year=1997|volume=104|issue=10|pages=912–917|url=http://www.mathcs.emory.edu/~ono/publications-cv/pdfs/023.pdf|accessdate=11 November 2012|doi=10.2307/2974471}} {{wayback|url=http://www.mathcs.emory.edu/~ono/publications-cv/pdfs/023.pdf |date=20151015193211 }}</ref> It is now known this is true if the [[generalized Riemann hypothesis]] is true.<ref name=Ken>{{cite journal|last=Ono|first=Ken|author2=K Soundararajan|title=Ramanujan's ternary quadratic forms|journal=Inventiones Mathematicae|year=1997|volume=130|issue=3|pages=415–454|url=http://mathcs.emory.edu/~ono/publications-cv/pdfs/025.pdf|accessdate=12 November 2012|doi=10.1007/s002220050191}} {{wayback|url=http://mathcs.emory.edu/~ono/publications-cv/pdfs/025.pdf |date=20190718155256 }}</ref>