###### tags: `MATA02-2022`
# MATA02-2022: Graded Assignment 3
**DUE: Friday, March 4, 11:59pm**

Note: I am aware that this is also the day of the midterm. Unfortunately, I did not know the midterm date when constructing my course calendar originally. As such, I'm making this homework super short, and I promise that working through these problems will be helpful practice for the midterm.

Note that you will have to show your work on the midterm. However, on Crowdmark, for questions 1-5, you just need to answer the question in the textbox.

Calculate the following in modular arithmetic:
1. $608 \times 298$ mod 7
2. $396 \times 437$ mod 439
3. $2945234 + 1497463$ mod 90
4. $515^2$ mod 519
5. $7^{32}$ mod 47
*Hint*: Don't try to brute-force this. Instead, try rewriting this as $((((7^2)^2)^2)^2)^2$
6. Find all the powers of 2 in modulo 23.
7. Find all the powers of 3 in modulo 23.