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.]

the f

last graph i believe

step-by-step explanation:

worked it out i believe

step-by-step explanation:

answers available in this download

(pearson%2c%25202012)%2520bbs.pdf& usg=aovvaw1obmtxnfghfgxhx0urh_je

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt