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Question: prove both the if and only if parts of proposition...

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Prove BOTH the if and only if parts of proposition 3.5.20: Proposition 3.5.20. Given a modular equation ax c (mod b), where a, b, c are integers. Then the equation has an integer solution for x if and only if c is an integer multiple of the greatest common divisor of a and b. Hint: You may use proposition 3.5.16 to help you: Proposition 3.5.16. Given the Diophantine equation an + bm -c, where a, b, c are integers. Then the equation has integer solutions for n and m if and only if c is a multiple of the gcd of a and b.

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