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Homework 11 Math 108, Spring 2015 Due Date: Saturday, May 9 1. Use a calculator to determine whether the given number is prime. If it is not prime, find two smaller numbers whose product is the given number. (a) 173 (b) 329 (c) 649 2. Use Excel to determine whether the given number is prime. If the number is not prime, find two smaller numbers whose product is the given number. (a) 8023 (b) 70,657 (c) 874,219 3. An encipherment formula is given. Find the corresponding decipherment formula. (You shouldn’t use Excel for this problem, but you may use a calculator.) (a) y ≡ x11 (mod 19) (b) y ≡ x13 (mod 31) (c) y ≡ x23 (mod 55) 4. Solve for x. Your answer should be between 0 and the given modulus. (You shouldn’t use Excel for this problem, but you may use a calculator.) (a) x7 ≡ 4 (mod 11) (b) x9 ≡ 3 (mod 23) (c) x11 ≡ 9 (mod 51) 5. Alice has chosen to use the RSA cryptosystem with modulus 187 and public key 23. What is her private key?