8.1. Understanding the functionality of groups, cyclic groups and subgroups is important for the use of public-key cryptosystems based on the discrete logarithm problem. That’s why we are going to practice some arithmetic in such structures in this set of problems. Let’s start with an easy one. Determine the order of all elements of the multiplicative groups of: 1. Z∗ 5 2. Z∗ 7 3. Z∗ 13

0.84 dang lotta people are looking for this lol or if you round up its 1 but the overall answer to that is 0.84

step-by-step explanation:

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

the answer is a.

135 and 80

step-by-step explanation:

56 44 2 4

step-by-step explanation: