Use the PCI to prove that
(a) every natural number greater than or equal to 11 can be written in the form 2s + 5t, for some natural numbers s and t.
(b) every natural number greater than 22 can be written in the form 3s + 4t, where s and t are integers, s ≥ 3 and t ≥ 2.
(c) every natural number greater than 33 can be written in the form 4s + 5t, where s and t are integers, s ≥ 3 and t ≥ 2.
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