Verify that Euler's theorem holds for all elements of Z_16 that are relatively prime to 16. What happens to the elements that are NOT relatively prime to 16? Use Euler's theorem to determine 8^223 mod 69. Explain clearly how you arrived at your answer. Bob's RSA parameters are n = 2491, p = 47, q = 53, b = 1607. He receives a ciphertext 997. Determine the plaintext. Use the square and multiply algorithm by hand (+basic calculator) and show all the steps