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Introduction to Number Theory  Homework on 2

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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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