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Proposition 5.5.29. Let n 1 be an integer, and let a be an element of Zn /0. Then ahas a multiplicative inverse in Zn if and only if god( a,n)=1 (that is, a is relatively prime to n). Let n 1 be an integer, and let a be an element of Zn \\ {0}. a. Prove the "only if" part of Proposition 5.5.29. That is, prove that if a has an inverse in Zn \\ {0} then god(a, n)=1. Use proposition 5.5.20 b. Prove the "if" part of Proposition 5.5.29. That is, prove that if god(a, n)=1 then a has an inverse in Zn \\ for. Proposition 5.5.20. Given a modular equation ax = c (mod b), where a, b, care 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