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Strong induction

Mathematical logic · Mathematics

Study notes

Q: Prove every n ≥ 1 postage ≥ 8 paise can be formed with 3 and 5 paise stamps (strong induction). Base: 8 = 3+5, 9 = 3+3+3, 10 = 5+5. Assume all amounts 8..k formable (k ≥ 10). For k+1: (k+1) - 3 = k-2 ≥ 8, formable by hypothesis; add a 3-paise stamp! So k+1 formable. (Weak induction fails: k might not relate to k-1 directly!)

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