Morera's theorem: Difference between revisions
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en>Daniele.tampieri m →References: Minor corrections |
The example has been removed as it is wrong. It's a basic result that if f(z) is analytic, then 1/f(z) is analytic anywhere f(z) is not zero. f(z) = z^2 is analytic and zero only at z = 0, thus g(z) = 1/f(z) = 1/z^2 is analytic in C not 0. |
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{{Infobox number | |||
| number = 105 | |||
| divisor = 1, 3, 5, 7, 15, 21, 35, 105 | |||
}} | |||
'''105''' ('''one hundred [and] five''') is the [[natural number]] following [[104 (number)|104]] and preceding [[106 (number)|106]]. | |||
==In mathematics== | |||
105 is a [[triangular number]], a [[polygonal number|12-gonal number]] and a [[Zeisel number]]. It is a [[sphenic number]], and is the product of three consecutive [[prime number]]s. 105 is the [[double factorial]] of 7. It is also the sum of the first five [[square pyramidal number]]s. | |||
105 comes in the middle of the [[prime quadruplet]] (101, 103, 107, 109). The only other such odd numbers less than a thousand are 15, 195 and 825. 105 is also a [[pseudoprime]] to the prime bases 13, 29, 41, 43, 71, 83 and 97. The distinct prime factors of 105 add up to 15, and so do those of 104, hence the two numbers form a [[Ruth-Aaron pair]] under the first definition. | |||
105 is also a number ''n'' for which <math>n - 2^k</math> is prime, for <math>0 < k < log_2(n)</math>. (This even works up to <math>k = 8</math>, ignoring the negative sign.) | |||
105 is the smallest integer such that the factorization of <math>x^n-1</math> over '''Q''' includes coefficients other than <math>\pm 1</math>. | |||
==In science== | |||
*The [[atomic number]] of [[dubnium]]. | |||
==In other fields== | |||
105 is also: | |||
* The number of [[sura]]t [[al-Fil]] in the [[Qur'an]].{{Citation needed|date=May 2010}} | |||
* A simple card game where players lose if they have over 105 points. | |||
* A [[Shimano#Road_groupsets|Shimano Road groupset]] since 1984 | |||
==See also== | |||
* [[List of highways numbered 105]] | |||
==References== | |||
* Wells, D. ''[[The Penguin Dictionary of Curious and Interesting Numbers]]'' London: Penguin Group. (1987): 134 | |||
{{Integers|1}} | |||
{{DEFAULTSORT:105 (Number)}} | |||
[[Category:Integers]] | |||
Revision as of 22:45, 16 September 2013
Template:Infobox number 105 (one hundred [and] five) is the natural number following 104 and preceding 106.
In mathematics
105 is a triangular number, a 12-gonal number and a Zeisel number. It is a sphenic number, and is the product of three consecutive prime numbers. 105 is the double factorial of 7. It is also the sum of the first five square pyramidal numbers.
105 comes in the middle of the prime quadruplet (101, 103, 107, 109). The only other such odd numbers less than a thousand are 15, 195 and 825. 105 is also a pseudoprime to the prime bases 13, 29, 41, 43, 71, 83 and 97. The distinct prime factors of 105 add up to 15, and so do those of 104, hence the two numbers form a Ruth-Aaron pair under the first definition.
105 is also a number n for which is prime, for . (This even works up to , ignoring the negative sign.)
105 is the smallest integer such that the factorization of over Q includes coefficients other than .
In science
- The atomic number of dubnium.
In other fields
105 is also:
- The number of surat al-Fil in the Qur'an.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.
- A simple card game where players lose if they have over 105 points.
- A Shimano Road groupset since 1984
See also
References
- Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134