Pillai’s conjecture

Target entity: Pillai’s conjecture
Context triple: [Ramanujan–Nagell equation, relatedTo, Pillai’s conjecture]

• A. Bateman–Horn conjecture
  The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
• B. Pólya’s conjecture
  Pólya’s conjecture is a disproven hypothesis in number theory that proposed a specific long-term sign pattern for the summatory Möbius function, suggesting it would eventually remain nonpositive.
• C. Erdős–Turán conjecture
  The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
• D. Hardy–Littlewood conjectures
  The Hardy–Littlewood conjectures are a collection of influential unproven hypotheses in analytic number theory that generalize the prime number theorem to describe the distribution of prime numbers and prime constellations.
• E. Erdős–Moser equation
  The Erdős–Moser equation is a famous unsolved Diophantine equation in number theory that asks whether 1^k + 2^k + ... + (m−1)^k = m^k has any integer solutions beyond the trivial case (k, m) = (1, 2).
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Pillai’s conjecture
Target entity description: Pillai’s conjecture is an unproven statement in number theory asserting that the difference between perfect powers takes each positive integer value only finitely many times.

• A. Bateman–Horn conjecture
  The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
• B. Pólya’s conjecture
  Pólya’s conjecture is a disproven hypothesis in number theory that proposed a specific long-term sign pattern for the summatory Möbius function, suggesting it would eventually remain nonpositive.
• C. Erdős–Turán conjecture
  The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
• D. Hardy–Littlewood conjectures
  The Hardy–Littlewood conjectures are a collection of influential unproven hypotheses in analytic number theory that generalize the prime number theorem to describe the distribution of prime numbers and prime constellations.
• E. Erdős–Moser equation
  The Erdős–Moser equation is a famous unsolved Diophantine equation in number theory that asks whether 1^k + 2^k + ... + (m−1)^k = m^k has any integer solutions beyond the trivial case (k, m) = (1, 2).
• F. None of above. chosen