Fascinating Fibonacci Facts
No two consecutive Fibonacci numbers have any common factors.
144 is the only square number in the entire infinite sequence (except 1).
8 is the only cubic number.
The sum of any ten consecutive Fibonacci numbers is always evenly divisible by 11.
Every 3rd Fibonacci number is divisible by 2.
Every 4th Fibonacci number is divisible by 3.
Every 5th Fibonacci number is divisible by 5.
Every 6th Fibonacci number is divisible by 8.
Every 7th Fibonacci number is divisible by 13.
Every 8th Fibonacci number is divisible by 21. (etc.)
Twice any Fibonacci number minus the next Fibonacci number equals the second number preceding the original one.
The product of any two alternating Fibonacci numbers differs from the square of the middle number by 1.
If Fibonacci numbers are squared and the adjacent squares are added together, a sequence of alternate Fibonacci numbers emerges.
The difference of the squares of alternate Fibonacci numbers is always a Fibonacci number.
For any four consecutive Fibonacci numbers, the difference of the squares of the middle two numbers equals the product of the outer two numbers.
For any three Fibonacci numbers, the sum of the cubes of the two greatest minus the cube of the smallest equals a Fibonacci number.
The sum of any number of Fibonacci numbers beginning with the first 1 is always equal to the second number beyond the last one added minus one.
The largest known Fibonacci prime number is the 571st number in the sequence -- a number of 119 digits.
These fun facts are from Trudi Garland's
Fascinating Fibonaccis.
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