3. Find x and y such that 314x + 159y = 1. 4. Find x and y such that 4144x + 7696y = 592. 5. If N = abc + 1, prove that (N, a) = (N, b) = (N, c) = 1. 6. Find two different solutions of 299x + 247y = 13. 7. Prove that if a b and bla, then a = b or a = -b. 8. Prove that if a b and a > 0, then (a, b) 9. Prove that ((a, b), b) (a, b). 10. = 11. = a. a. Prove that (n, n + 1) = 1 for all n > 0. b. If n > 0, what can (n, n + 2) be? a. Prove that (k, n +k) 1 if and only if (k, n) = 1. b. Is it true that (k, n + k) = d if and only if (k, n) = d? 12. Prove: If a b and c|d, then ac bd. =

Determine whether there appears to be a Main Effect for IV-A by writing “YES” or“NO”  Determine whether there appears to be a Main Effect for IV-B by writing “YES” or“NO”

Answer the following questions, similar to those found in problem 23 of section 2.3 in your text. Assume that there are 10 girls and 11 boys in the neighborhood club, and a team of 7 is to be selected. (1) How many different teams can be selected? (2) How many different teams can be selected if each team must contain exactly 3 girls and 4 boys? (3) How many different teams can be selected if each team must contain both boys and girls?

Problem. 11: Compute the product. -4 1 -10