divisibilty_properties

Interesting Divisibility Properties

Here is a list of the first 20 Fibonacci numbers:

F₁= 1

F₆= 8

F₁₁= 89

F₁₆= 987

F₂= 1

F₇= 13

F₁₂= 144

F₁₇= 1597

F₃= 2

F₈= 21

F₁₃= 233

F₁₈= 2584

F₄= 3

F₉= 34

F₁₄= 377

F₁₉= 4181

F₅= 5

F₁₀= 55

F₁₅= 610

F₂₀= 6765

Which Fibonacci numbers are divisible by 2? What is the pattern?

Which Fibonacci numbers are divisible by 3? What is the pattern?

Which Fibonacci numbers are divisible by 5? What is the pattern?

Without looking at the list, which Fibonacci numbers do you predict will be divisible by 8?

What is the pattern in general? I.e., which Fibonacci numbers do you predict will be divisible by F_n, the nth Fibonacci number?

F₁= 1	F₆= 8	F₁₁= 89	F₁₆= 987
F₂= 1	F₇= 13	F₁₂= 144	F₁₇= 1597
F₃= 2	F₈= 21	F₁₃= 233	F₁₈= 2584
F₄= 3	F₉= 34	F₁₄= 377	F₁₉= 4181
F₅= 5	F₁₀= 55	F₁₅= 610	F₂₀= 6765