## Description

Math 422: Introduction to Number Theory

Homework on 2

1. A circular dial has the numbers 0 through 56 inscribed at equal intervals

along the rim.

(a) A grasshopper sits at the 0. It can jump 5 units in either direction

(clockwise or counterclockwise) any number of times. What is the

set of numbers that the grasshopper can reach with a sequence of

jumps?

(b) Same question, but instead the grasshopper can only jump 3 units

at a time.

2. Silverman 2.1.

3. Silverman 2.5.

4. Silverman 3.2.

5. Silverman 5.1.

6. Silverman 5.6. The proof should be very short!

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