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Question: this is a twopart proof with parts a and b...

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This is a two-part proof, with parts a and b: Let n > 1 be an integer, and let a be an element of Zn 10] a) Prove the only if part of Proposition 3.5.29 Proposition 3.5.29. Letn > 1 be an integer, and let a be an element of Zn \[0]. Then a has an inverse in Zn if and only ifgcd(a, n)-1 (that is, a is relatively prime to n). That is, prove that if a has an inverse in Zn、〈0} then gcd(a, n)-1. [Hint: You can use 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 b) Prove the if part of Proposition 3.5.29. That is, prove that if gcd(a, n)-1 then a has an inverse in Zn \ {0}

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