a. Prove: If a and d are positive integers and q and r are

Chapter 4, Problem 22E

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QUESTION: Prove: If a and d are positive integers and q and r are integers such that a = dq + r and 0 < r < d, then?a = d(?(q + 1)) + (d ? r )and0 < d ? r < d.b. Indicate how to modify Algorithm 4.8.1 to allow for the input a to be negative.

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QUESTION: Prove: If a and d are positive integers and q and r are integers such that a = dq + r and 0 < r < d, then?a = d(?(q + 1)) + (d ? r )and0 < d ? r < d.b. Indicate how to modify Algorithm 4.8.1 to allow for the input a to be negative.

ANSWER:

Solution:

Step 1:

In this question we have to prove an equality and use this to modify Algorithm 4.8.1 to allow for the input a to be negative.

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