Mason–Stothers theorem

Target entity: Mason–Stothers theorem
Context triple: [abc conjecture, relatedTo, Mason–Stothers theorem]

• A. Faltings' theorem
  Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
• B. Pillai’s conjecture
  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.
• C. Bombieri–Lang conjecture
  The Bombieri–Lang conjecture is a major unsolved conjecture in number theory and arithmetic geometry predicting that varieties of general type over number fields have only finitely many rational points.
• D. Baker theorem on linear forms in logarithms
  The Baker theorem on linear forms in logarithms is a fundamental result in transcendental number theory that provides explicit lower bounds for nonzero linear combinations of logarithms of algebraic numbers, with powerful applications to Diophantine equations and Diophantine approximation.
• E. Mordell–Weil theorem
  The Mordell–Weil theorem is a fundamental result in number theory stating that the group of rational points on an abelian variety (in particular, an elliptic curve) over a number field is finitely generated.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Mason–Stothers theorem
Target entity description: The Mason–Stothers theorem is a result in algebraic function theory that gives a sharp relation between the degrees of three coprime polynomials satisfying A + B = C and the number of distinct roots of their product, and serves as a polynomial analogue of the abc conjecture.

• A. Faltings' theorem
  Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
• B. Pillai’s conjecture
  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.
• C. Bombieri–Lang conjecture
  The Bombieri–Lang conjecture is a major unsolved conjecture in number theory and arithmetic geometry predicting that varieties of general type over number fields have only finitely many rational points.
• D. Baker theorem on linear forms in logarithms
  The Baker theorem on linear forms in logarithms is a fundamental result in transcendental number theory that provides explicit lower bounds for nonzero linear combinations of logarithms of algebraic numbers, with powerful applications to Diophantine equations and Diophantine approximation.
• E. Mordell–Weil theorem
  The Mordell–Weil theorem is a fundamental result in number theory stating that the group of rational points on an abelian variety (in particular, an elliptic curve) over a number field is finitely generated.
• F. None of above. chosen