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).)

Rhombus adef is inscribed into a triangle abc so that they share angle a and the vertex e lies on the side bc . what is the length of the side of the rhombus if ab=c, and ac=b.

Asix-sided number cube is rolled twice. what is the probability that the first roll is an even numbe and the second roll is a number greater than 4?

I've been working on this for a few days and i just don't understand, it's due in a few hours. you.the direction of a vector is defined as the angle of the vector in relation to a horizontal line. as a standard, this angle is measured counterclockwise from the positive x-axis. the direction or angle of v in the diagram is α.part a: how can you use trigonometric ratios to calculate the direction α of a general vector v = < x, y> similar to the diagram? part bsuppose that vector v lies in quadrant ii, quadrant iii, or quadrant iv. how can you use trigonometric ratios to calculate the direction (i.e., angle) of the vector in each of these quadrants with respect to the positive x-axis? the angle between the vector and the positive x-axis will be greater than 90 degrees in each case.part cnow try a numerical problem. what is the direction of the vector w = < -1, 6 > ?