Question

Let f_n be the nth Fibonacci number. Use induction, show that, f_n is divisible by 3 if and only if n is divisible by 4.

          Let f_n be the nth Fibonacci number. Use induction, show that,

f_n is divisible by 3 if and only if n is divisible by 4.

Added by Mary B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

10/08/2023

Step 1

So the statement holds for the base case. Inductive step: Assume that the statement holds for some $n = 4k$, where $k$ is a positive integer. That is, $f_{4k}$ is divisible by 3. We want to show that $f_{4(k+1)}$ is also divisible by 3. We know that $f_{4k} = Show more…

Show all steps