Question

Solve the congruence 9x ≡ 21 (mod 12) listing all the incongruent solutions. 2. Prove that the system of congruences x ≡ a1 (mod m1) and x ≡ a2 (mod m2) can be solved if and only if (m1, m2) divides a1 − a2. Prove furthermore that the solution, when it exists, is unique modulo m: [m1, m2].

Name: 1 solve the congruence 9x 21 mod 12 listing all the incongruent solutions 2 prove that the system of congruences x a1 mod m1 and x a2 mod m2 can be solved if and only if m1 m2 divides a1 a2 11884
Uploaded: 2022-06-16T09:26:25-08:00
Duration: 6 min 7 s
Channel: Madhur L
Description: 1 solve the congruence 9x 21 mod 12 listing all the incongruent solutions 2 prove that the system of congruences x a1 mod m1 and x a2 mod m2 can be solved if and only if m1 m2 divides a1 a2 11884

          Solve the congruence 9x ≡ 21 (mod 12) listing all the incongruent solutions.

2. Prove that the system of congruences x ≡ a1 (mod m1) and x ≡ a2 (mod m2) can be solved if and only if (m1, m2) divides a1 − a2. Prove furthermore that the solution, when it exists, is unique modulo m: [m1, m2].

Added by Nicole D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/16/2022

Step 1

Solve the congruence 9x ≡ 21 (mod 12) First, we simplify the congruence by reducing 9 and 21 modulo 12. We get: 9x ≡ 21 (mod 12) => -3x ≡ 9 (mod 12) We can multiply both sides by -1 to get: 3x ≡ -9 (mod 12) => 3x ≡ 3 (mod 12) Then, we divide both sides by 3 Show more…

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Solve the congruence 9x ≡ 21 (mod 12) listing all the incongruent solutions. 2. Prove that the system of congruences x ≡ a1 (mod m1) and x ≡ a2 (mod m2) can be solved if and only if (m1, m2) divides a1 − a2. Prove furthermore that the solution, when it exists, is unique modulo m: [m1, m2].