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people:fer:330ws:330ws_homework

## Math 330 - 02 Homework

• LaTeX-ed solutions are encouraged and appreciated.
• If you use LaTeX, hand-in a printed version of your homework.
• You are encouraged to discuss homework problems with classmates, but such discussions should NOT include the exchange of any written material.
• Writing of homework problems should be done on an individual basis.
• References to results from the textbook and/or class notes should be included.
• The following lists should be considered partial and tentative lists until the word complete appears next to it.
• Use 8.5in x 11in paper with smooth borders. Write your name on top of each page. Staple all pages.


Problem Set 7 (partial) Due: 10/27/2017. Board presentation: 11/??/2017

1. Prove the corollary to Prop. 6.25: Let $a,b\in\Z$, $n\in\N$ and $k\geq 0$. If $a \equiv b \pmod{n}$ then $a^k \equiv b^k \pmod{n}$. (Hint: induction on $k$)
2. Prove Prop. 8.6

Problem Set 6 (complete) Due: 10/13/2017. Board presentation: 10/20/2017

1. Let $f_n$ be the $n$-th Fibonacci number. Prove by induction on $n$ that $\sum_{j=1}^n f_{2j} = f_{2n+1}-1$
2. Find and write down all the partitions on a 4-element set $A=\{a,b,c,d\}$. How many equivalence relations are there on $A$?
3. Prove Prop. 6.15
4. Prove Prop. 6.16
people/fer/330ws/330ws_homework.txt · Last modified: 2017/10/20 12:53 by fer