Hello, i'm new to the forum. I'm currently majoring in Math at my local university. I'm taking a math course called Discrete Mathematical Structures and have some homework questions which i'm having trouble solving. I was hoping someone could help me in solving them and explain how they got to that point.
1. Use mathematical induction to prove that: 4^(n) - 1 is divisible by 3 for all n.
2. Use mathematical induction to prove that: 1+2+...+n<((n+1)/2)
3. Use induction to prove the following statement: "If p is a prime and p divides a^(n) for n>1, then p must divide a itself."
4. Prove that the sum of two prime numbers, each larger than 2, is not a prime number. (Note: This does not require induction)
Any help is appreciated, and thanks to anyone and everyone in advance.