In section 1.2, we learned the about proofs based on induction. These problems will help you practice.
1. Prove that $5 \cdot 12^{n} + 8 \cdot 38^{n}$ is evenly divisible by 13 for all non-negative integer values of $n$.

2. Prove that $3 \cdot 19^{n} + 7 \cdot 9^{n}$ is evenly divisible by 10 for all non-negative integer values of $n$.

3. Prove that $2 \cdot 11^{n} + 3 \cdot 26^{n}$ is evenly divisible by 5 for all non-negative integer values of $n$.

4. Prove that $5 \cdot 27^{n} + 2 \cdot 34^{n}$ is evenly divisible by 7 for all non-negative integer values of $n$.

5. Prove that $4 \cdot 27^{n} + 9$ is evenly divisible by 13 for all non-negative integer values of $n$.

6. Prove that the sum of the odd numbers 1 to n is a perfect square using induction.