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Determine whether the following congruences have an integer solution. You do not need to find an actual solution. 1. X? = 127 (11 · 547). 2. X² = 127 (3 · 7 · 73). 3. X? = 781 (112 . 31). 4. X² = 781 (11 ·614).

Determine whether the following congruences have an integer solution. You do not need to find an actual solution. 1. X? = 127 (11 · 547). 2. X² = 127 (3 · 7 · 73). 3. X? = 781 (112 . 31). 4. X² = 781 (11 ·614).

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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Determine whether the following congruences have an integer solution. You do not need to find an actual solution. 1. X? = 127 (11 · 547). 2. X² = 127 (3 ·7 · 73). 3. X? = 781 (11² · 31). 4. X? = 781 (11 · 614).
Transcribed Image Text:Determine whether the following congruences have an integer solution. You do not need to find an actual solution. 1. X? = 127 (11 · 547). 2. X² = 127 (3 ·7 · 73). 3. X? = 781 (11² · 31). 4. X? = 781 (11 · 614).
Note: 547, 73, 31, 61, 41 and 43 are all prime.
Transcribed Image Text:Note: 547, 73, 31, 61, 41 and 43 are all prime.
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