# Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

## Unique Properties of 125

- 125 is the smallest cube which is also a sum of distinct non-zero squares: 125 = 5
^{3}= 11^{2}+ 2^{2} - 125 is the smallest hypotenuse for which there exist exactly 3 distinct Pythagorean triangles
- 125 is the smallest face diagonal of the smallest Euler brick
- 125 is the smallest number n such that n
^{n}contains a pandigital substring - 125 is the smallest cube with the same set of digits as another cube (512)
- 125 is the smallest cube that is sandwiched between two non-squarefree numbers: 124 = 2
^{2}* 31, 125 = 5^{3}, 126 = 2 * 3^{2}* 7 (submitted by Massimo Koffler) - 125 can be written in a non-trivial way using its own digits: 125 = 5
^{1+2}. Such numbers are called Friedman numbers, and 125 is a third Friedman number