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It all depends on what you're counting. Sort algorithm analysis typically counts key comparisons or record movement. In radixsort (and trie algorithms in general), you are relying on operations on digits of the key, not comparisons of entire keys. So linear isn't necessarily wrong, but you do have to say what you're counting.

Number theory? Not seeing the connection.

It wasn't number theory, but I couldn't remember and was hand-waving.

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