The Euler Phi-Function Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Find the value of the Euler phi-function for the integer 100.

(2) Find the value of the Euler phi-function for the integer 256.

(3) Find the value of the Euler phi-function for the integer 1001.

(4) Find the value of the Euler phi-function for the integer .

(5) Find the value of the Euler phi-function for the integer

(6) Find the value of the Euler phi-function for the integer

(7) Show that

(8) Find all positive integers such that

(9) Find all positive integers such that

(10) Show that if and are positive integers, then   

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