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 n2 + 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.