In Mathematics
Sixty-five is the 23rd semiprime and the 3rd of the form (5.q)it is an octagonal number. It is also a Cullen number. Given 65, the Mertens function returns 0.
Sixty-five has an aliquot sum of 19 and is the first composite number in the 19-aliquot tree.
This number is the magic constant of 5 by 5 normal magic square:
This number is also the magic constant of n-Queens Problem for n = 5.
65 is the smallest integer that can be expressed as a sum of two distinct positive squares in two ways, 65 = 82 + 12 = 72 + 42.
It appears in the Padovan sequence, preceded by the terms 28, 37, 49 (it is the sum of the first two of these).
There are only 65 known Euler's idoneal numbers.
65=15+24+33+42+51
65 is the length of the hypotenuse of 4 different pythagorean triangles, the lowest number to have more than 2: 652 = 162 + 632 = 332 + 562 = 392 + 522 = 252 + 602. The first two are "primitive", and 65 is the lowest number to be the largest side of more than one such triple.
Read more about this topic: 65 (number)
Famous quotes containing the word mathematics:
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
If bread and butter wanted weight;
And wisely tell what hour o’ th’ day
The clock doth strike, by algebra.”
—Samuel Butler (1612–1680)
“The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.”
—Willard Van Orman Quine (b. 1908)