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Let k be an integer such that k = -1 (mod 5). What is the remainder when 50k10 + 26k³ – 17 is divided by 5? What is the last digit of the base 5 representation of k? Why?

Let k be an integer such that k = -1 (mod 5). What is the remainder when 50k10 + 26k³ – 17 is divided by 5? What is the last digit of the base 5 representation of k? Why?

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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Page 8. 13. Let k be an integer such that k = -1 (mod 5). (a, What is the remainder when 50k10 + 26k³ – 17 is divided by 5? (b), What is the last digit of the base 5 representation of k? Why? Use induction to prove that TD + 22+ + n 14.. 1(1+1) + 3(3+1) n(n+1) for all integers n > 1. п+1 + Drag and drop an image or PDF file or click to browse...
Transcribed Image Text:Page 8. 13. Let k be an integer such that k = -1 (mod 5). (a, What is the remainder when 50k10 + 26k³ – 17 is divided by 5? (b), What is the last digit of the base 5 representation of k? Why? Use induction to prove that TD + 22+ + n 14.. 1(1+1) + 3(3+1) n(n+1) for all integers n > 1. п+1 + Drag and drop an image or PDF file or click to browse...
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