1. Prove that 9 n – 4 n is a multiple of 5 for all n ∈ . 2. Prove that 12 n – 5 n is a multiple of 7 for all n ∈ . 3. If a, b, and c ∈ N such that a – b is a multiple of c, prove that a n – b n is a...

1. Prove that 9ⁿ
– 4ⁿ
is a multiple of 5 for all n ∈
.

2. Prove that 12ⁿ
– 5ⁿ
is a multiple of 7 for all n ∈
.

3. If a, b, and c ∈ N such that a – b is a multiple of c, prove that aⁿ
– bⁿ
is a multiple of c for all n ∈
.

4. Prove that
 + 5 + 8 +L + (3n −1) = 2 n(3n +1) for all n ∈
.