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From Wikipedia, the free encyclopedia

21 (twenty-one) is the natural number following 20 and preceding 22.

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Transcription

Contents

In mathematics

21 is:

Note that a necessary condition for n is that for any a coprime to n, a and n - a must satisfy the condition above, therefore at least one of a and n - a must only have factor 2 and 5.

Let donate the quantity of the numbers smaller than n that only have factor 2 and 5 and that are coprime to n, we instantly have .

We can easily see that for sufficiently large n, , but , as n goes to infinity, thus fails to hold for sufficiently large n.

In fact, For every n > 2, we have

and

so fails to hold when n > 273 (actually, when n > 33).

Just check a few numbers to see that n = 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 21.

21 appears in the Padovan sequence, preceded by the terms 9, 12, 16 (it is the sum of the first two of these).[8]

In science

Age 21

  • In several countries 21 is the age of majority. See also: Coming of age.
  • In all US states, 21 is the drinking age.
    • However, in Puerto Rico and U.S. Virgin Islands, the drinking age is 18.
  • In California, Hawaii, New York, and New Jersey, 21 is the minimum age that one person may purchase cigarettes and other tobacco products.
  • In some countries it is the voting age.
  • In the United States, 21 is the age at which one can purchase multiple tickets to an R-rated film without providing identification. It is also the age to accompany one under the age of 17 as their parent or adult guardian for an R-rated movie.
  • In most US states, 21 is the minimum age at which a person may gamble or enter casinos.
  • In 2011, Adele named her second studio album 21, because of her age at the time.
  • In the United Kingdom, 21 is the minimum age to accompany a learner driver, provided that the person supervising the learner has held a full driving licence for a minimum of three years.

In sports

In other fields

Building called "21" in Zlín, Czech Republic.
Building called "21" in Zlín, Czech Republic.
Detail of the building entrance
Detail of the building entrance

21 is:

References

  1. ^ "Sloane's A016105 : Blum integers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  2. ^ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  3. ^ "Sloane's A005349 : Niven (or Harshad) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  4. ^ "Sloane's A001006 : Motzkin numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  5. ^ "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  6. ^ "Sloane's A000567 : Octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  7. ^ C. J. Bouwkamp, and A. J. W. Duijvestijn, "Catalogue of Simple Perfect Squared Squares of Orders 21 Through 25." Eindhoven University of Technology, Nov. 1992.
  8. ^ "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
This page was last edited on 31 July 2019, at 10:49
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