Law of Quadratic Reciprocity 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) Evaluate the Legendre symbol

(2) Evaluate the Legendre symbol

(3) Evaluate the Legendre symbol

(4) Evaluate the Legendre symbol   

(5) Evaluate the Legendre symbol   

(6) Evaluate the Legendre symbol   

(7) Using the law of quadratic reciprocity, show that if is an odd prime. Then

(8) Using the law of quadratic reciprocity, show that if is an odd prime. Then

(9) Find a congruence describing all primes for which 5 is a quadratic residue.

(10) Find a congruence describing all primes for which 7 is a quadratic residue.

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