Modulo Arithmet ic a: Prove or disprove the following functions are well-defined: f: Z4Z6 given by f()= [2x+ 1 *f: Z12Z4 given by f() = [2x + 1] b: Prove: For all integers a and n, if gcd(a, n) as...

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Extracted text: Modulo Arithmet ic a: Prove or disprove the following functions are well-defined: f: Z4Z6 given by f()= [2x+ 1 *f: Z12Z4 given by f() = [2x + 1] b: Prove: For all integers a and n, if gcd(a, n) as 1mod n). The integer s is called the inverse of a modulo n 1, then there exists an integer s such that c: Find a positive inverse for 3 modulo 40. That is, find a positive integer s such that 3s = 1 mod 40)