Fifty is the smallest number that can be written as the sum of two squares in two distinct ways: 50 = 12 + 72 = 52 + 52. It is also the sum of three squares, 50 = 32 + 42 + 52. It is a Harshad number.
There is no answer to the equation φ(x) = 50, making 50 a nontotient. Nor is there an answer to the equation x - φ(x) = 50, making 50 a noncototient.
The Saros number (http://sunearth.gsfc.nasa.gov/eclipse/SEsaros/SEsaros1-175.html) of the solar eclipse series which began on 1201February 11 BC and ended on 97April 1. The duration of Saros series 50 was 1298.1 years, and it contained 73 solar eclipses.
The Saros number (http://sunearth.gsfc.nasa.gov/eclipse/LEsaros/LEsaros1-175.html) of the lunar eclipse series which began on -1134July 3 and ended on 164August 20. The duration of Saros series 50 was 1298.1 years, and it contained 73 lunar eclipses.
In other fields
Fifty is also:
The traditional number of years in a default jubilee period.
A calibre of ammunition (0.50 inches: see .50 BMG)
In millimeters, the focal length of the normal lens in 35mm photography.
the percentage equivalent to one half, so that the phrase "fifty-fifty" commonly expresses something divided equally in half, or an event of probability one half