1) i'm gonna skip step 1, so...
Assume TRUE for n = k
Therefore 9^(k+2) - 4^k = 5M, M being any integer
Prove for n=k+1
Therefore:
9^(k+3) - 4^(k+1)
= 9*9(k+2) - 4*4^k
=9(5M + 4^k) - 4*4^k --> From the assumption, 5M + 4^k = 9^(k+2)
=45M + 9*4^k - 4*4^k
=45M + 5*4^k
=5(9M + 4^k)...