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- Tijdeman's_theorem abstract "In number theory, Tijdeman's theorem states that there are at most a finite number of consecutive powers. Stated another way, the set of solutions in integers x, y, n, m of the exponential diophantine equationfor exponents n and m greater than one, is finite.The theorem was proven by Dutch number theorist Robert Tijdeman in 1976, making use of Baker's method in transcendence theory to give an effective upper bound for x,y,m,n. Michel Langevin computed a value of exp exp exp exp 730 for the bound.Tijdeman's theorem provided a strong impetus towards the eventual proof of Catalan's conjecture by Preda Mihăilescu. Mihăilescu's theorem states that there is only one member to the set of consecutive power pairs, namely 9=8+1.That the powers are consecutive is essential to Tijdeman's proof; if we replace the difference of 1 by any other difference k and ask for the number of solutionsof with n and m greater than one we have an unsolved problem, called the generalized Tijdeman problem. It is conjectured that this set also will be finite. This would follow from a yet stronger conjecture of Pillai (1931), see Catalan's conjecture, stating that the equation only has a finite number of solutions. The truth of Pillai's conjecture, in turn, would follow from the truth of the abc conjecture.".
- Tijdeman's_theorem wikiPageID "5001103".
- Tijdeman's_theorem wikiPageRevisionID "559385848".
- Tijdeman's_theorem hasPhotoCollection Tijdeman's_theorem.
- Tijdeman's_theorem subject Category:Diophantine_equations.
- Tijdeman's_theorem subject Category:Theorems_in_number_theory.
- Tijdeman's_theorem type Abstraction100002137.
- Tijdeman's_theorem type Communication100033020.
- Tijdeman's_theorem type DiophantineEquations.
- Tijdeman's_theorem type Equation106669864.
- Tijdeman's_theorem type MathematicalStatement106732169.
- Tijdeman's_theorem type Message106598915.
- Tijdeman's_theorem type Proposition106750804.
- Tijdeman's_theorem type Statement106722453.
- Tijdeman's_theorem type Theorem106752293.
- Tijdeman's_theorem type TheoremsInNumberTheory.
- Tijdeman's_theorem comment "In number theory, Tijdeman's theorem states that there are at most a finite number of consecutive powers. Stated another way, the set of solutions in integers x, y, n, m of the exponential diophantine equationfor exponents n and m greater than one, is finite.The theorem was proven by Dutch number theorist Robert Tijdeman in 1976, making use of Baker's method in transcendence theory to give an effective upper bound for x,y,m,n.".
- Tijdeman's_theorem label "Stelling van Tijdeman".
- Tijdeman's_theorem label "Teorema di Tijdeman".
- Tijdeman's_theorem label "Tijdeman's theorem".
- Tijdeman's_theorem sameAs Tijdemanova_věta.
- Tijdeman's_theorem sameAs Teorema_di_Tijdeman.
- Tijdeman's_theorem sameAs Stelling_van_Tijdeman.
- Tijdeman's_theorem sameAs m.0cz8qc.
- Tijdeman's_theorem sameAs Q777924.
- Tijdeman's_theorem sameAs Q777924.
- Tijdeman's_theorem sameAs Tijdeman's_theorem.
- Tijdeman's_theorem wasDerivedFrom Tijdeman's_theorem?oldid=559385848.
- Tijdeman's_theorem isPrimaryTopicOf Tijdeman's_theorem.