Английская Википедия:105 (number): различия между версиями
(Новая страница: «{{Английская Википедия/Панель перехода}} {{Infobox number | number = 105 | divisor = 1, 3, 5, 7, 15, 21, 35, 105 }} '''105''' ('''one hundred [and] five''') is the natural number following 104 and preceding 106. ==In mathematics== 105 is a triangular number, a dodecagonal number,<ref>{{Cite web|url=https://oeis.org/A051624|title=Sloane's A051624 : 12-gonal numbers|website=The On-...») |
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Текущая версия от 05:01, 18 декабря 2023
Шаблон:Infobox number 105 (one hundred [and] five) is the natural number following 104 and preceding 106.
In mathematics
105 is a triangular number, a dodecagonal number,[1] and the first Zeisel number.[2] It is the first odd sphenic number and is the product of three consecutive prime numbers. 105 is the double factorial of 7.[3] 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 numbers less than a thousand are 9, 15, 195, and 825.
105 is also the middle of the only prime sextuplet (97, 101, 103, 107, 109, 113) between the ones occurring at 7-23 and at 16057–16073. As the product of the first three odd primes (<math>3\times5\times7</math>) and less than the square of the next prime (11) by > 8, for <math>n=105</math>, n ± 2, ± 4, and ± 8 must be prime, and n ± 6, ± 10, ± 12, and ± 14 must be composite (prime gap).Шаблон:Clarification needed
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 non-zero coefficients other than <math>\pm 1</math>. In other words, the 105th cyclotomic polynomial, Φ105, is the first with coefficients other than <math>\pm 1</math>.
105 is the number of parallelogram polyominoes with 7 cells.[4]
In science
- The atomic number of dubnium.
In other fields
105 is also:
- A Shimano Road groupset since 1984
See also
References
- Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134