Fibonacci numbers

Question

Find integers N and M (other than N = 1, M = 1) satisfying:

 

a) the equation F_N = M²

 

b) the equation F_N = (F_M)³

Answer 1

Again, the only way I see is to write the list and look for perfect squares and cubes.

 

For part a) N = 12, M = 12, F₁₂ = 144

 

Part b) N = 6, M = 3

F₃ = 2,    F₆ = 8