Unexpected

Alice, Bob, and Carol are really close friends; in fact, they are so close, they even share the same primes in their RSA public keys! Alice has N = P*Q, Bob has N = QR, and Carol has N = PR, where P,Q,R are 1024 bit primes. All three also use the same public exponent e = 65537. Can you recover the three ciphertexts?

Use flagCheck to input the flag you get from the challenge to get the actual flag