(b) Consider the system of linear congruences below: x = 2 (mod 5) 2x = 22 (mod 8) 3x = 12 (mod 21) (i) How many solutions does it have lying between 0 and 1679? (ii) Determine two different systems of linear congruences for which the Chi- nese Remainder Theorem can be used and which will give at least two of these solutions.
(b) Consider the system of linear congruences below: x = 2 (mod 5) 2x = 22 (mod 8) 3x = 12 (mod 21) (i) How many solutions does it have lying between 0 and 1679? (ii) Determine two different systems of linear congruences for which the Chi- nese Remainder Theorem can be used and which will give at least two of these solutions.
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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Transcribed Image Text:(b) Consider the system of linear congruences below:
x = 2 (mod 5)
2x = 22 (mod 8)
3x = 12 (mod 21)
(i) How many solutions does it have lying between 0 and 1679?
(ii) Determine two different systems of linear congruences for which the Chi-
nese Remainder Theorem can be used and which will give at least two
of these solutions.
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