CSCE 423/823 (Fall 2019) Homework 0

You may discuss general course concepts with your classmates, but you must solve the problems on your own and write up your own solutions in your own words and acknowledge anyone whom you consulted. Clarity of presentation is important. You should give clear answers to all exercises. You must submit your solutions in a single pdf file via Canvas, and are encouraged to prepare your solutions in LaTeX. Only pdf will be accepted, and you should only submit one pdf file.

1. (5 points) Give positive integer values for a, b, c, and d that satisfy the equation a⁴ + b⁴ + c⁴ = d⁴.
2. (5 points) Summarize Prof. Leighton's definition of proof by contradiction.
3. (5 points) Summarize Prof. Leighton's definition of proof by induction.
4. (5 points) Summarize Prof. Leighton's definition of an invariant.
5. (5 points) Summarize four of Prof. Leighton's ten proof techniques that should never be used.
6. (10 points) This semester, you will work on your future homeworks in teams of size 2–4. For this exercise, list your teammates' names. Your teams should be homogeneous with respect to your class, i.e., each team should consist of only students from CSCE 423 or from 823.