Suppose that (n, e) is an rsa encryption key, with n = pq, where p and q are large primes and gcd(e, (p − 1)(q − 1)) = 1. furthermore, suppose that d is an inverse of e modulo (p − 1)(q − 1). suppose that c ≡ me (mod pq). in the text we showed that rsa decryption, that is, the congruence cd ≡ m (mod pq) holds when gcd(m, pq) = 1. show that this decryption congruence also holds when gcd(m, pq) > 1. [hint: use congruences modulo p and modulo q and apply the chinese remainder theorem.]

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls

cant

step-by-step explanation: there is no picture