a) State the Chinese remainder theorem.________________b)

Chapter 5, Problem 13RQ

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QUESTION:

a) State the Chinese remainder theorem.________________b) Find the solutions to the system x ? 1 (mod 4), x = 2 (mod 5), and x ? 3 (mod 7).

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QUESTION:

a) State the Chinese remainder theorem.________________b) Find the solutions to the system x ? 1 (mod 4), x = 2 (mod 5), and x ? 3 (mod 7).

ANSWER:

SOLUTIONStep 1Chinese Remainder theorem Let be a collection of pairwise relatively prime integers.Then the system of simultaneous congruences... has a unique solution modulo P = for any given integers .b)Step 1 We have to find the solution to the following system

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