Describe how to select public and private keys

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Explain the RSA Public Key Encryption Scheme in detail.In particular ,how do the encryption and decryption algorithms work? Explain also how you choose the public and private keys.Suppose a user picks n=17*5; i.e .,p=17 and q=5.How should he pick the public key and the private key (i.e., d and e)? Give the encryption and decryption algorithms.