# 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 768

- 768 is the smallest number n such that n times n+1 gives the concatenation of two numbers m and m+2 (768*769 = 590592)
- 768 is the number of distinct Hadamard matrices of order 4
- 768 is the smallest area of a cyclic quadrilateral PQRS with non-increasing sequence of sides PQ, QR, RS, and SP, such that the area, the sides, the radius of the circumcircle, and the two diagonals are integers

## Common Properties of 768

The number n is *abundant* if the sum of all its positive divisors except itself is more than n.

They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.

A positive integer greater than 1 that is not prime is called *composite*.

Composite numbers are opposite to prime numbers.

A number is *even* if it is divisible by 2.

Numbers that are not even are odd. Compare with another pair -- evil and odious numbers.

The number n is *evil* if it has an even number of 1's in its binary expansion.

Guess what odious numbers are.

The number n is *practical* if all numbers strictly less than n are sums of distinct divisors of n.

The *untouchable* numbers are those that are not the sum of the proper divisors of any number.