Question 2 (2pts)


F(n+1)=F(n)+F(n-1)  n>1,   F(0)=0, F(1)=1 is another form of defining the Fibonacci sequence.

I want to perform the following iterative process.
Let A0=F(n+1), A1=F(n).

step 1. Divide A0=F(n+1) by A1 = F(n) to generate a quotient 
Q1 and a remainder A2 (as given by division),

step 2 iteratively divide A1 by A2 to give a new quotient  Q2 and remainder  A3.

step 3 etc repeat by dividing A2 with A3 with generated quotient Q3, and  remainder A4. Process stops when for some
i,   Ai is equal to 0.

[Given than R1 > R2 > ... the remainders form a decreasing sequence and thus eventually 0 will be reached]

Question: How many division steps to reach a remainder that is 0 ?

 

Example  for non fibonacci  A=44, B=8

44 = 8 * 5 + 4

  8 = 4 * 2 + 0

implies two division steps to reach a 0 remainder.


Feb 2, 2022 @17:48