1. Suppose that p is a positive integer. Write the following statement using quantifiers where possible. Then write its negation.

"For any positive integer r < p such that there exists some integer k with kr = p, then r = 1 must hold."

2. Prove the following theorem directly. “If a is an odd integer, then 4 is a divisor of 3a ² + 10a + 3”

3. For the following statement, write down the hypothesis and the conclusion, and then state the contrapositive of the statement. Prove the statement by contraposition. " If c is an odd integer then the equation x ² + x - c = 0 has no integer solution."