Final answer:
The question involves using an encryption function with modular arithmetic, which is often used in cryptography. Unfortunately, without clearer context or the original message to apply this function to, an accurate solution cannot be determined solely from the details provided.
Step-by-step explanation:
The student is asking how to identify the number obtained after applying the encryption function f(p)= (p + 13) mod 26 to the letter-number translation provided in the options. The letter-number scheme likely follows A=1, B=2, ..., Z=26. To solve this, each number in the options would be increased by 13 and then the sum would be taken modulo 26 to find the 'encrypted' number.
However, without a direct reference to the starting message or the exact encryption scheme used for the original numbers, we cannot provide a precise answer to which option is correct. The question seems to involve understanding and applying modular arithmetic, which is a key concept in cryptography. The miscellaneously provided numbers and equations, which do not seem immediately relevant, cannot be used in this context without additional context tying them to the encryption scheme.