Faster algorithm to find unique element between two arrays?

Question

EDIT: For anyone new to this question, I have posted an answer clarifying what was going on. The accepted answer is the one I feel best answers my question

Answer 1

There simply is no faster algorithm. The ones presented in the question are in O(n). Any arithmetic "trick" to solve this will require at least each element of both arrays to be read once, so we stay in O(n) (or worse).

Any search strategy that is in a real subset of O(n) (like O(log n)) will require sorted arrays or some other prebuild sorted structure (binary tree, hash). All sorting algorithms known to mankind are at least O(n*log n) (Quicksort, Hashsort) at average which is worse than O(n).

Therefore, from a mathematical point of view, there is no faster algorithm. There might be some code optimizations, but they won't matter on large scale, as runtime will grow linear with the length of the array(s).