Chinese Remainder Theorem 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 an integer that leaves remainder of 1 when divided by either 2 or 5, but that is divisible by 3.

(2) Find all the solutions of the system of linear congruence equations:

(3) Find all the solutions of the system of linear congruence equations:

(4) Find all the solutions of the system of linear congruence equations:

(5)  Find all the solutions of the system of linear congruence equations:

(6) Find all the solutions to the system of linear congruence equations and

(7) If eggs are removed form a basket 2, 3, 4, 5, and 6, at a time, there remain, respectively, 1, 2, 3, 4, and 5 eggs. But if the eggs are removed 7 at a time, no eggs remain. What is the least number of eggs that could have been in the basket?

(8) Find an integer that leaves remainder of 9 when it is divided by either 0 or 11, but that is divisible by 3.

(9) Find all the solutions of the system of linear congruence equations:

(10) Find all the solutions of the system of linear congruence equations:

(11)  Find all the solutions of the system of linear congruence equations:

(12)  Find all the solutions of the system of linear congruence equations:

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