In that case, their test suite doesn’t cover all relevant cases. Consider nums = [1,1,1,1,4]: There are 5 elements, so n=4, and all elements are within the range [1,4]; only the 1 is duplicated. This fulfills all of the listed requirements.

The actual sum is 8, and the 4th triangular number is 10, so the duplicated number according to your algorithm must be -2 (or some fraction thereof, depending on how you calculate m).