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7. (Problem 3 on page 341 from Rosen) Let P(n) be the statement that a postage...

7. (Problem 3 on page 341 from Rosen) Let P(n) be the statement that a postage of n cents can be formed using just 3-cent stamps and 5-cent stamps. The parts of this exercise outline a strong induction proof that P(n) is true for n ³ 8.

  • Show that the statements P(8), P(9), and P(lO) are true, completing the basis step of the proof.
  • What is the inductive hypothesis of the proof?
  • What do you need to prove in the inductive step?

Complete the inductive step for k ³ 10.

Explain why these steps show that this formula is true whenever n ³ 8.

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