(a) If the tuple (a, b, c) satisfy the following conditions: a, b and c are consecutive odd integers. a, b and c are all primes. Then we call it a...

(a) If the tuple (a, b, c) satisfy the following conditions: • a, b and c are consecutive odd integers. • a, b and c are all primes. Then we call it a super prime tuple. Prove that (3, 5, 7) is the only super prime tuple. (b) Define F0 = 0, F1 = 1, Fn+2 = Fn+1 + Fn for n = 0, 1, 2, …. Prove that for any n ≥ 0 we have Fn ≤ ((1 + 5 )/2)n – 1.