Content deleted Content added
DuncanHill (talk | contribs) Fixing harv/sfn error introduced in preceding edit. ref = {{SfnRef|Carmichael|1914}} and {{sfn whitelist|CITEREFCarmichael1914}}. Please watchlist Category:Harv and Sfn no-target errors and install User:Trappist the monk/HarvErrors.js to help you spot such errors when reading and editing. |
Will Orrick (talk | contribs) It was a mistake to use sfn, as it's not used elsewhere in the article. Change style of sfn footnote to match other footnotes. |
||
Line 157:
:<math>a^{2^{k-2}}\equiv 1\pmod{2^k}.</math>
It provides that {{math | ''λ''(2<sup>''k''</sup>)}} is at most {{math | 2<sup>''k'' − 2</sup>}}.
===Average value===
Line 242:
===Minimal order===
For any sequence {{math | ''n''<sub>1</sub> < ''n''<sub>2</sub> < ''n''<sub>3</sub> < ⋯}} of positive integers, any constant {{math | 0 < ''c'' < {{sfrac|1|ln 2}}}}, and any sufficiently large {{mvar | i}}:<ref name="Theorem 1 in Erdős (1991)">Theorem 1 in Erdős (1991)</ref><ref name=HBII193>Sándor & Crstici (2004) p.193</ref>
:<math>\lambda(n_i) > \left(\ln n_i\right)^{c\ln\ln\ln n_i}.</math>
Line 251:
Moreover, {{mvar | n}} is of the form
:<math>n=\mathop{\prod_{q \in \mathbb P}}_{(q-1)|m}q</math>
for some square-free integer {{math | ''m'' < (ln ''A'')<sup>''c'' ln ln ln ''A''</sup>}}.<ref name="Theorem 1 in Erdős (1991)"/>
===Image of the function===
Line 273:
* {{cite journal |first1=John B. |last1=Friedlander |author1-link=John Friedlander |first2=Carl |last2=Pomerance |first3=Igor E. |last3=Shparlinski |year=2001 |title=Period of the power generator and small values of the Carmichael function |journal=Mathematics of Computation |volume=70 |number=236 |pages=1591–1605, 1803–1806 |mr=1836921 | zbl=1029.11043 | issn=0025-5718 |doi=10.1090/s0025-5718-00-01282-5|doi-access=free }}
* {{cite book | last1=Sándor | first1=Jozsef | last2=Crstici | first2=Borislav | title=Handbook of number theory II | ___location=Dordrecht | publisher=Kluwer Academic | year=2004 | isbn=978-1-4020-2546-4 | pages=32–36, 193–195 | zbl=1079.11001}}
* {{Gutenberg|no=13693|name=The Theory of Numbers|last=Carmichael|first=Robert D.|origyear=
{{Totient}}
| |||