# 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 2015

- 2015 the smallest positive integer n for which there are two two-digit numbers x and y comprised of four different non-zero digits such that: n = x
^{2} − y^{2} = reverse(x)^{2} − reverse(y)^{2} (submitted by Alex Ryba)

## Common Properties of 2015

The number n is called an *apocalyptic power* if 2^{n} contains the consecutive digits 666 (in decimal).

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.

A number is said to be *square-free* if its prime decomposition contains no repeated factors.