Chapter 13, Problem 15E

Fact: If we make a list of any four consecutive Fibonacci numbers, the first one times the fourth one is always equal to the third one squared minus the second one squared.

a. Verify this fact for the list $F_8,F_9,F_{10},F_{11}$.

b. Using the list $F_N$, $F_{N+1}$, $F_{N+2}$, $F_{N+3}$, write this fact as a mathematical formula.