Use mathematical induction in Exercises 31-37 to prove di- visibility facts. 31. Prove that 2 divides n2 +n whenever n is a positive in- teger. 32. Prove that 3 divides n'+ 2n whenever n is a positive...

Extracted text: Use mathematical induction in Exercises 31-37 to prove di- visibility facts. 31. Prove that 2 divides n2 +n whenever n is a positive in- teger. 32. Prove that 3 divides n'+ 2n whenever n is a positive integer. 33. Prove that 5 divides n° n whenever n is a nonnegative integer. 34. Prove that 6 divides n integer. n whenever n is a nonnegative