# Solutions to Problem Set 9

Math 345/504

2-14-2018

1. Compute . Simplify your answer to a number in the range .

Hence, .

2. Solve the modular equation .

Multiplying by 9, I get

3. Solve the modular equation . Simplify your answer to a number in the range . Show your work!

Divide out the common factor of 6, and divide the modulus by :

To get solutions mod 106, add multiples of 53: Thus, .

The solutions are .

Fanaticism consists in redoubling your effort when you have forgotten your aim. - George Santayana

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