Need Help Tutoring With Math Prove and Problem Solving

I want a person who can help me with everything related to my study for math subject until Mid-December. If you can prove/solve the attached question then i will hire you!

Topics:
1. Logic
2. Set Theory
3. Quantifiers
4. Laws of Arithmetic
5. Diophantine Equations and Elementary Number Theory
6. Bezout’s Identity
7. Euclidian Lemma Etc.

Topics like proving gcd etc.