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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 is True orFalse. If True, write a proof. If False, exhibit acounterexample.

1) If m, n are arbitrary positive integers, then any system ofform

x ≡ a (mod m)

x ≡ b (mod n)

has a solution.

2) If m, n are arbitrary positive integers and the system

x ≡ a (mod m)

x ≡ b (mod n)

has a solution, then the solution is unique modulo mn. ModernAbstract Algebra

modern algebra

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