# 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 65

- 65 is the smallest number that becomes square if its reverse is either added to or subtracted from it
- 65 is the smallest composite number of the form n
^{2} + 1, where n is even
- 65 is the magic constant of the 5 by 5 magic square
- 65 is the smallest hypotenuse of two different primitive Pythagorean triangles (33, 56, 65 and 16, 63, 65)

## Common Properties of 65

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.