Catalan's conjecture
Conjetura de Catalan
- Date
- 1842 · confidence high
- Place
- École Polytechnique, Paris, France
- Credited to
- Eugène Charles Catalan
- Field
- Knowledge & symbols
What was discovered
Catalan conjectured that 8 and 9 are the only pair of consecutive perfect powers among the natural numbers, i.e. that the equation x^a - y^b = 1 has only that solution with x, y, a, b integers greater than 1. Preda Mihailescu proved it in 2002, now known as Mihailescu's theorem.
Catalan was then an assistant professor (répétiteur) at the École Polytechnique in Paris; the conjecture remained unproven for 160 years, until Preda Mihailescu proved it in 2002 (published in 2004).
What it led to
- Mihailescu's theorem (2002), closing the conjecture after 160 years
- A boost to the study of cyclotomic fields and Galois modules