6. Let p,q be distinct odd primes and let (m) = [p 1,q 1], the least common multiple of p 1 and q 1. Suppose we set up an RSA cryptosystem with modulus m = pq and an encrypting exponent e coprime to p1 and q1. Show that if d is a solution of the congruence ex 1 (mod (m)), then d is a suitable decrypting exponent for e. (Hint: show that d works modulo p and modulo q.)