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Given the diagram below and knowing that point E lies on side AC, and point D lies on BE. If BC = n and DB

Given the diagram below and knowing that point E lies on side AC, and point D lies on BE.

If BC = n and DB = n − 1 for some positive integer n and ∠ABC = ∠ACB = ∠CED = ∠CDE.

Find the number of positive integers n with 2023 < n < 10 000 for which the length of AB is also an integer.

B D A E C

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