Properties of the number 50

Question

I will shortly be engaging with my 50th (!) birthday.

50 = 1+49 = 25+25 can perhaps be described as a "sub-Ramanujan" number.

I'm trying to put together a quiz including some mathematical content. Contributions most welcome. What does 50 mean to you?

Answer 1

Fifty is the smallest number that is the sum of two non-zero square numbers in two distinct ways: $$50 = 1^2 + 7^2 = 5^2 + 5^2$$

Answer 2

There is an integral solution to the Mordell equation $y^2 = x^3 + 50$ with $x=-1,$ but nothing integral for $y^2 = x^3 - 50.$ There are rational solutions, however, beginning with $x=211/9.$ The group of rational points on this elliptic curve is infinite cyclic.

On the other hand, what 50 really means to me is that doctors in the U.S. begin to push you to do tests that are just, um, undignified.

Answer 3

$50$ is the sum of three consecutive squares: $50=3^2+4^2+5^2$

Answer 4

$50$ is the least integer that is $1$ more than a square but is not squarefree.

Answer 5

$50$ is the sum of the first $3$ Abundant numbers.

Answer 6

1 + 3 + 5 + 7 + 9 + 9 + 7 + 5 + 3 + 1 = 50