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1. Consider two integers m = 9k – 2 andn = 3k- 2, where k is a fixed odd integer. Find gcd(m, n). Show reasoning. 2. Let a, b, c, k, l be integers with a # 0. Show that if al b and al c, then alkb + lc. 3. Let a = 6! + 7! + ...+ 103!. What is the remainder when a is divided by 13? Show reasoning.

1. Consider two integers m = 9k – 2 andn = 3k- 2, where k is a fixed odd integer. Find gcd(m, n). Show reasoning. 2. Let a, b, c, k, l be integers with a # 0. Show that if al b and al c, then alkb + lc. 3. Let a = 6! + 7! + ...+ 103!. What is the remainder when a is divided by 13? Show reasoning.

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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1. Consider two integers m = 9k – 2 andn 3k- 2, where k is a fixed odd integer. Find gcd(m, n). Show reasoning. 2. Let a, b, c, k, l be integers with a # 0. Show that if al b and al c, then alkb + lc. 3. Let a = 6! + 7! + ...+ 103!. What is the remainder when a is divided by 13? Show reasoning.
Transcribed Image Text:1. Consider two integers m = 9k – 2 andn 3k- 2, where k is a fixed odd integer. Find gcd(m, n). Show reasoning. 2. Let a, b, c, k, l be integers with a # 0. Show that if al b and al c, then alkb + lc. 3. Let a = 6! + 7! + ...+ 103!. What is the remainder when a is divided by 13? Show reasoning.
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