Find the duplicate number without modifying the array

You are handed an array nums of length $n+1$ where every value is between $1$ and $n$ inclusive. By the pigeonhole principle at least one value repeats, and in this problem exactly one value repeats (possibly many times).

Find the duplicate using $O(1)$ extra space, without modifying the array. Sorting or a hash set are the easy answers, the interviewer wants neither.