Catalan's conjecture [SEP] discoverer or inventor
Catalan's conjecture
Catalan's conjecture (or Mihăilescu's theorem) is a theorem in number theory that was conjectured by the mathematician Eugène Charles Catalan in 1844 and proven in 2002 by Preda Mihăilescu. The integers 2 and 3 are two powers of natural numbers whose values (8 and 9, respectively) are consecutive. The theorem states that this is the "only" case of two consecutive powers. That is to say, that the only solution in the natural numbers of
for "a", "b"
, , , , e, ln , 2, "e", Catalan's constant, or Khinchin's constant rational, algebraic irrational, or transcendental? What is the irrationality measure of each of these numbers?
- Vitushkin's conjecture
- Invariant subspace problem
- Kung–Traub conjecture
Unsolved problems Combinatorics.
- Frankl's union-closed sets conjecture: for any family of sets closed under sums there exists an element (of the underlying space) belonging to half or more of the sets
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