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 = 53 = 112 + 22
- 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 nn 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 = 22 * 31, 125 = 53, 126 = 2 * 32 * 7 (submitted by Massimo Koffler)
- 125 can be written in a non-trivial way using its own digits: 125 = 51+2. Such numbers are called Friedman numbers, and 125 is a third Friedman number