Question: Let a0 = 3, b0 = 4, and c0 = 5. a) Let ak = ak-1 + 2, bk = 2ak-1 + bk-1 + 2,

Let a0 = 3, b0 = 4, and c0 = 5.
a) Let ak = ak-1 + 2, bk = 2ak-1 + bk-1 + 2, and ck = 2ak-1 + ck-1 + 2 for ∈ N. Prove that ck - bk is constant for all k ∈ N.
b) Prove that the numbers defined in part a) satisfy
a2k + b2k = c2k
for all k ∈ N.

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