Triangle $ABC$ has a perimeter of 2007 units. The sides have lengths that are all integer values with $AB< BC \leq AC$. What is the smallest possible value of $BC - AB$?
Question:
Triangle $ABC$ has a perimeter of 2007 units. The sides have lengths that are all integer values with $AB< BC \leq AC$. What is the smallest possible value of $BC - AB$?
Answer:
Let's think step by step.

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Triangle $ABC$ has a perimeter of 2007 units. The sides have lengths that are all integer values with $AB< BC \leq AC$. What is the smallest possible value of $BC - AB$?
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