I’m working on a Computer Science question and need guidance to help me study.

Use Sage to answer the following questions. Show all your sage input/output:

- Suppose your RSA public key factors as p = 6569 and q = 8089, and the public exponent e is 11. Suppose you were sent the Ciphertext 28901722. Perform the RSA Decryption and recover the plaintext.
- Suppose that you want to encrypt the number 449 and send it to someone with public key N =37617577, and e = 529
- Suppose that you forgot your public exponent, but you know that the prime factors of your Key’s modulus are 1723 and 5381 private exponent is 223. Find the public exponent.
- Use sage to generate an rsa public / private key pair and perform an encryption and decryption.