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Determine whether each of the following statements is True or False. If True, write a proof....

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Advance Math

Determine whether each of the following statements isTrue or False. If True, write a proof. If False, exhibit acounterexample.

1) If m, n are arbitrary positive integers, then anysystem of form

x ≡ a (mod m)

x ≡ b (mod n)

has a solution.



2) If m, n are arbitrary positive integers and thesystem

x ≡ a (mod m)

x ≡ b (mod n)

    has a solution, then thesolution is unique modulo mn.

Modern Abstract Algebra

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