MATH 380 Exercise3
1. Find the periods of the sequences {un}(mod m) for m = 2 to m = 12.
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m |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
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period |
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Do you see any patterns?
2. i. For which n is 
un º
0 (mod 3)? Make a conjecture.
ii. For which n is
un º
0 (mod 4)? Make a conjecture.
iii. For which n
is un º
0 (mod 5)? Make a conjecture.
3. Homework – Due Thursday, September 9
a) Prove:
If a, b, c, and d are integers and m > 1 with a º b (mod m) and c º d (mod m) , then
i) a + c º b + d (mod m)
ii) ac º bd (mod m)
b) Prove:
I would like volunteers to present the following results from Exercise 2 during Thursday’s class. The results are #2 and 3. Let me know before class if you would like to present.
2. 
3.
