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In an RSA system the public key of a given user is e = 31, n = 3599. What is the private key of this user?

In an RSA system the public key of a given user is e = 31, n = 3599. What is the private key of this user? Correct Answer 3031

By trail and error, we determine that p = 59 and q = 61. Hence f(n) = 58 x 60 = 3480. Then, using the extended Euclidean algorithm, we find that the multiplicative inverse of 31 modulo f(n) is 3031.

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