Using the Division Algorithm, prove that for any positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b

Let x be positive integer. Prove If x2 + 1 is even, then x3 is odd

Prove 8 divides 34h+1+52h+1 whenever h is a positive integer

Use the theorem that we proved to prove the following “extended" version, which holds for positive and negative divisors: Theorem (Division Algorithm For Nonzero Divisors). Let a and n be integers with n #0. Then there exist unique integers q and r such that a = qn + r аnd 0