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Let a, b be positive integers. How many multiples of b are there in the sequence Prove your answer. a, 2a, 3a, .... ba?

Let a, b be positive integers. How many multiples of b are there in the sequence Prove your answer. a, 2a, 3a, .... ba?

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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Need help with these two Difficult Intro to Elementary Number Theory Homework problems.

 

Let a, b be positive integers. How many multiples of b are there in the sequence Prove your answer. a, 2a, 3a, ba? ..."
Transcribed Image Text:Let a, b be positive integers. How many multiples of b are there in the sequence Prove your answer. a, 2a, 3a, ba? ..."
Determine if the linear congruences below have solutions or not. A. 168x10 (mod 139) B. 123x2 = 91 (mod 117) C. -168x3 = 72 (mod 132) D. 195x4= -92 (mod 165) Enter the number abcd below, where • a = 0 if A. does not have a solution, a = 1 if A. has a solution, • b = 0 if B. does not have a solution, b = 1 if B. has a solution, • c = 0 if C. does not have a solution, c = 1 if C. has a solution, d = 0 if D. does not have a solution, d = 1 if D. has a solution. For example, if all of them have solutions enter 1111 and if none of them have solutions enter 0000. Type your answer...
Transcribed Image Text:Determine if the linear congruences below have solutions or not. A. 168x10 (mod 139) B. 123x2 = 91 (mod 117) C. -168x3 = 72 (mod 132) D. 195x4= -92 (mod 165) Enter the number abcd below, where • a = 0 if A. does not have a solution, a = 1 if A. has a solution, • b = 0 if B. does not have a solution, b = 1 if B. has a solution, • c = 0 if C. does not have a solution, c = 1 if C. has a solution, d = 0 if D. does not have a solution, d = 1 if D. has a solution. For example, if all of them have solutions enter 1111 and if none of them have solutions enter 0000. Type your answer...
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