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) Prove the existence part of the division algorithm. That is, show for n E Z, d E Z+, there exist integers q,r such that n = qd +r with 00 using induction on n, then employ this case to obtain the result for negative integers as well.)

) Prove the existence part of the division algorithm. That is, show for n E Z, d E Z+, there exist integers q,r such that n = qd +r with 00 using induction on n, then employ this case to obtain the result for negative integers as well.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please use induction thanks!

(2) Prove the existence part of the division algorithm. That is, show for n E Z, d E Zt, there exist integers q,r such that n = 0<r<d. (HINT: First prove this in the case n >0 using induction on n, then employ this case to obtain the result for negative integers as well.) qd +r with
Transcribed Image Text:(2) Prove the existence part of the division algorithm. That is, show for n E Z, d E Zt, there exist integers q,r such that n = 0<r<d. (HINT: First prove this in the case n >0 using induction on n, then employ this case to obtain the result for negative integers as well.) qd +r with
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