Question: Question 5: In this question we will discuss the multiplicative properties of the Euler function. For a given positive integer n let Un={kN:1kn1,gcd(k,n)=1}. (a) Compute

Question 5: In this question we will discuss the multiplicative properties

Question 5: In this question we will discuss the multiplicative properties of the Euler function. For a given positive integer n let Un={kN:1kn1,gcd(k,n)=1}. (a) Compute (n) for n{3,5,7,15,21,35}. Verify that (15)=(3)(5),(21)=(3)(7),(35)=(5)(7). (b) Let m,n be positive integers with gcd(m,n)=1. Use the Chinese remainder theorem to give a bijection between the Cartesian product UmUn and the set Umn

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