Instructions Solve at least 2 problems by induction. Problems Question 1. Prove that n2 - 4n + 3 2 0 for any n > 3 Question 2. Prove that 9" + 7 is divisible by 8 for any n 2 0 Question 3. Prove that n2 - 9n + 20 > 0 for any n > 5 Question 4. Prove that 3" + 5 is divisible by 2 for any n > 0 Question 5. Prove that n2 - 2n > 0 forany n > 2 Question 6. Prove that 10" - 7 is divisible by 3 for any n 2 4 Question 7. Prove that n' + 4n -5 2 0 for any n > 1 Question 8. Prove that 3" - 9 is divisible by 2 for any n > 3 Question 9. Prove that n' + n - 12 > 0 for any n > 3 Question 10. Prove that 4" - 7 is divisible by 3 for any n > 1 Question 11. Prove that 9" + 7 is divisible by 8 for any n 2 0 Question 12. Prove that 3" + 5 is divisible by 2 for any n 2 0 Question 13. Prove that 10" - 7 is divisible by 3 for any n > 4 Question 14. Prove that 3" - 9 is divisible by 2 for any n > 3 Question 15. Prove that 4" - 7 is divisible by 3 for any n 2 1