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Here is another version of the Quotient-Remainder Theorem: Given any integers n, d with d 0, there exist unique integers q, r satisfying (1) n = dq + r (2) -d/2

Here is another version of the Quotient-Remainder Theorem: Given any integers n, d with d 0, there exist unique integers q, r satisfying (1) n = dq + r (2) -d/2

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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Here is another version of the Quotient-Remainder Theorem: Given any integers n, d with d ‡ 0, there exist unique integers q, r satisfying (1) n = dq + r (2) -d/2 <r<d/2 Find the quotient and remainder (using the theorem above!) for the following pairs of integers: n = 11, d = 2 q= n = 11, d = 3 q= n = -11, d = 3 q= n= 54 d = 7 q= n= -54 d = 7 q= n= 52 d=8 q= n = -52 d = 8 q= 7 r = r = r = r= r= r= r=
Transcribed Image Text:Here is another version of the Quotient-Remainder Theorem: Given any integers n, d with d ‡ 0, there exist unique integers q, r satisfying (1) n = dq + r (2) -d/2 <r<d/2 Find the quotient and remainder (using the theorem above!) for the following pairs of integers: n = 11, d = 2 q= n = 11, d = 3 q= n = -11, d = 3 q= n= 54 d = 7 q= n= -54 d = 7 q= n= 52 d=8 q= n = -52 d = 8 q= 7 r = r = r = r= r= r= r=
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