Let p be an odd prime and let g be a primitive root modulo p (i. e., F ∗ p = {1, g, g2 , . . . , gp−2}), and let a be an integer. (a) Prove that if the discrete logarithm log (a) is even, then a has a square root modulo p. (I. e., there exists an integer b such that b 2 ≡ a (mod p).)

In the polynomial below, what number should replace the question mark to produce a difference of squares? x2 + ? x - 36

If you could answer these your a life saver

Suppose that 3% of all athletes are using the endurance-enhancing hormone epo (you should be able to simply compute the percentage of all athletes that are not using epo). for our purposes, a “positive” test result is one that indicates presence of epo in an athlete’s bloodstream. the probability of a positive result, given the presence of epo is .99. the probability of a negative result, when epo is not present, is .90. what is the probability that a randomly selected athlete tests positive for epo? 0.0297