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7. Prove that for all n ∈ N, if n ≥ 12 then there are k,...

7. Prove that for all n ∈ N, if n ≥ 12 then there are k, ` ∈ N such that 4k + 5` = n. (Hint: use strong induction on the set {n ∈ N : n ≥ 12}, but first prove the result directly for n = 12, 13, 14, and 15.

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By induction if n 12 then there are k, y such that n= 4k+5y

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