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Catalan's conjecture, also known as Mihăilescu's theorem, states that the only solution in positive integers to the equation \( x^a - y^b = 1 \), where \( a \) and \( b \) are integers greater than 1, is the pair \( (3, 2) \) for the values \( (x, y) \) and \( (a, b) = (3, 2) \).

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  1. Diophantine equations
  2. Number theory
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