# 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 76

- 76 is the only number n that can be partitioned into distinct primes in exactly n ways
- 76 is the largest two-digit automorphic number

## Rare Properties of 76

The number n is called an *automorphic* number if (the decimal expansion of) n^{2} ends with n. These numbers are also called *curious*.

It is curious, how for a k-digit automorphic number n there is another automorphic number -- 10^{k} + 1 - n. For this to work with n=1, you have to treat 1 as a zero-digit number.

## Common Properties of 76

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.

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 *odious* if it has an odd number of 1's in its binary expansion.

Guess what evil numbers are.