Since gcd(7, 20) = 1 and 7·3 = 21 ≡ 1 (mod 20), e is valid with d = 3, and 4^{21} ≡ 4 (mod 33). The option claiming invalidity relies on a wrong gcd computation.
The RSA cryptosystem is a public-key encryption method based on the difficulty of factoring the product of two large primes. It uses Euler's theorem and modular inverses to encrypt and decrypt messages.
\[c \equiv m^{e} \pmod{n}, \quad m \equiv c^{d} \pmod{n}\]