21 (number)


21 is the natural number following 20 and preceding 22.

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.
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.

In science

21 is: