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3. Exercise 52.3 #40. Prove that the system of linear congruences in one variable given by z= b, mod m, z= by mod ma z= b, mod m. is solvable if and only if (m, m,)|b, – b, for all i # j. In this case, prove that the solution is unique modulo [m, m2. m

3. Exercise 52.3 #40. Prove that the system of linear congruences in one variable given by z= b, mod m, z= by mod ma z= b, mod m. is solvable if and only if (m, m,)|b, – b, for all i # j. In this case, prove that the solution is unique modulo [m, m2. m

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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3. Exercise $2.3 #40. Prove that the system of linear congruences in one variable given by z= bị mod my 1= b, mod ma 1= b, mod ma is solvable if and only if (m, m,) |b, – b, for all i + j. In this case, prove that the solution is unique modulo [m1, mą. ..,m„)
Transcribed Image Text:3. Exercise $2.3 #40. Prove that the system of linear congruences in one variable given by z= bị mod my 1= b, mod ma 1= b, mod ma is solvable if and only if (m, m,) |b, – b, for all i + j. In this case, prove that the solution is unique modulo [m1, mą. ..,m„)
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