Solving Polynomial Congruences 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 all solutions of the polynomial congruence equation:

(2) Find all solutions of the polynomial congruence equation:

(3) Find all solutions of the polynomial congruence equation:

(4) Find all solutions of the polynomial congruence equation:

(5) Find all solutions of the polynomial congruence equation:

(6) Find all solutions of the polynomial congruence equation:

(7) Find all solutions of the polynomial congruence equation:

(8) Find all solutions of the polynomial congruence equation:

(9) Find all solutions of the polynomial congruence equation:

(10) Find all solutions of the polynomial congruence equation:

(11) Find all solutions of the polynomial congruence equation:  

(12) Find all solutions of the polynomial congruence equation:

(13) How many incongruent solutions are there to the polynomial congruence equation

(14) How many incongruent solutions are there to the polynomial congruence equation

(15) Let be an integer and a prime such that Use Hensel's lemma to solve the polynomial congruence equation for all positive integer

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