(2) When should the enterpriser retire the machine? (15%)

題組內容

1. An enterpriser plans to purchase one new machine for 500 dollars. When the machine is retired at time T, its salvage value is S(T) = 300 - 20T. The machine yields a quasi-rent flow at the rate R_t = 80 - 4t dollars per year. Assuming that the rate of interest is 4%.

1. (20%) Consider an RSA cryptographic system with the public key \( (n, e) = (649, 387) \). First, find prime numbers \( p \) and \( q \) such that \( n = pq \). Second, find the value of \( d \) in the private key \( (n, d) \). Third, decrypt the ciphertext 10 into plaintext. Fourth, encrypt the plaintext 351 into ciphertext. Finally, answer the question "Is it possible to find more than one values of \( d \) in the range \( 0 < d < (p - 1)(q - 1) \) that works in decryption?" If your answer is YES, find all possible values of \( d \); if your answer is NO, give a brief proof.

題組內容

(2) When should the enterpriser retire the machine? (15%)

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