Tijdeman's theorem

Tijdeman's theorem is a result in number theory concerning the equation \( x^k - y^m = 1 \), where \( x \), \( y \) are positive integers, and \( k \), \( m \) are integers greater than or equal to 2. The theorem states that the only solutions in positive integers \( (x, y, k, m) \) to this equation occur for certain specific values.