1 establish the assertion 4Fn if and only if 6n hint use Fib

1) establish the assertion: 4/Fn if and only if 6/n (hint: use Fibonacci in determing this question)

Solution

gcd (Fn, Fm)= Fd where d= gcd (n,m) Verify this identity in the case of gcd (F9, F12) and gcd(F15, F20) 6. 4/Fn if and only if 6/n

F1 = 4/6 =2/3

F2 = 6/2/3 =9

but gcd of gcd (F9, F12)  is not 6