Use induction to prove the Division Algorithm. (Hint: Suppose that n is a fixed

Question

Use induction to prove the Division Algorithm. (Hint: Suppose that n is a fixed natural numberand use induction on the m.) Other information: Division Algorithm - Let n and m be natural numbers withn < m. There exists anatural number q so that m = qn or there exists natural number q and rso that m = qn + r where r is a naturalnumber with r<n I'm having some trouble on the inductive step...I can't seemto find a way to set this up so that I can show that m+1=nq fromthe restrictions... Any help would be most appreciated. (Hint: Suppose that n is a fixed natural numberand use induction on the m.) Other information: Division Algorithm - Let n and m be natural numbers withn < m. There exists anatural number q so that m = qn or there exists natural number q and rso that m = qn + r where r is a naturalnumber with r<n I'm having some trouble on the inductive step...I can't seemto find a way to set this up so that I can show that m+1=nq fromthe restrictions... Any help would be most appreciated. I'm having some trouble on the inductive step...I can't seemto find a way to set this up so that I can show that m+1=nq fromthe restrictions... Any help would be most appreciated.

Explanation / Answer

Then m + 1 = qn + r + 1.
Separate into two cases. One where r +1 < n and one where r +1 = n. Hope that helps. Let me know if you need more detail.

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