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)
Rare Properties of 125
The number n is a cube if it is the cube of an integer.
Common Properties of 125
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime numbers.
The number n is deficient if the sum of all its positive divisors except itself is less than n.
Compare with perfect and abundant numbers.
The number n is evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
A number is odd if it is not divisible by 2.
Numbers that are not odd are even. Compare with another pair -- evil and odious numbers.
An integer n is powerful if for every prime p dividing n, p2 also divides n.
How much power? They all can be written as a2 b3.