Exercise 2.10. Prove the division theorem by induction. (Hint: Take a to be a fixed positive integer and let b vary. Prove the theorem for varying b by induction. First treat the case b = 1. Then assume that the theorem is true for a given b and show that it holds for b+1.) The division theorem can be strengthened by adding a statement about the uniqueness of q and r:

Q: part 2 of question

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