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One way to uniquely combine two integers into a single integer through a deterministic process is by using concatenation. We can concatenate the two integers in a specific order and convert the resulting string into an integer. For example, if we have two integers 123 and 456, we can concatenate them in the order 123456 to obtain the integer 123456.

Another way to combine two integers into a single integer is by using prime factorization. We can assign each prime number a unique digit, and then write the prime factorization of each integer using these digits. Then we can concatenate the two resulting strings and convert the concatenated string into an integer. For example, if we have two integers 28 and 35, we can assign the digit 2 to the prime number 2, and the digit 3 to the prime number 3. Then we can write the prime factorizations of 28 and 35 as 223 and 35, respectively. Finally, we can concatenate these two strings to obtain the string 22335 and convert it into the integer 22,335.