Use the table of indices modulo 37 to find all solutions to the following congruences. (c) x12 = 11 (mod 37) (d) 7x20 = 34 (mod 37) 12x 23 (mod 37) 5x23 18 (mod 37)
Use the table of indices modulo 37 to find all solutions to the following congruences. (c) x12 = 11 (mod 37) (d) 7x20 = 34 (mod 37) 12x 23 (mod 37) 5x23 18 (mod 37)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 59RE
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Question
![28.1. Use the table of indices modulo 37 to find all solutions to the following congruences.
x12= 11 (mod 37)
7x20 = 34 (mod 37)
(a) 12x = 23 (mod 37)
(b)
5x23 = 18 (mod 37)
(c)
(d)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91f76606-a4d9-42f0-be0d-7b1366a5593f%2Feae83ed0-7bad-4f96-b1d0-e9722c965d6a%2F1730vn_processed.png&w=3840&q=75)
Transcribed Image Text:28.1. Use the table of indices modulo 37 to find all solutions to the following congruences.
x12= 11 (mod 37)
7x20 = 34 (mod 37)
(a) 12x = 23 (mod 37)
(b)
5x23 = 18 (mod 37)
(c)
(d)
![1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
a
I(a) 36 1 26 2 23 27 32 3 16 24 30 28 11 33 13 4
17 18
7 17
a
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
I (a) 35 25 22 31 15 29 10 12 6 34 21 14 9 5 20 8 19 18
Table of Indices Modulo 37 for the Base 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91f76606-a4d9-42f0-be0d-7b1366a5593f%2Feae83ed0-7bad-4f96-b1d0-e9722c965d6a%2F6rxpbrs_processed.png&w=3840&q=75)
Transcribed Image Text:1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
a
I(a) 36 1 26 2 23 27 32 3 16 24 30 28 11 33 13 4
17 18
7 17
a
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
I (a) 35 25 22 31 15 29 10 12 6 34 21 14 9 5 20 8 19 18
Table of Indices Modulo 37 for the Base 2
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