Catalan's Conjecture

• Κύριος συγγραφέας: Schoof, René (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: London : Springer London : Imprint: Springer, 2008.
• Έκδοση: 1.
• Σειρά: Universitext,
• Θέματα: Mathematics.; Algebra.; Number theory.; Number Theory.; General Algebraic Systems.; Mathematics, general.

Eugène Charles Catalan made his famous conjecture – that 8 and 9 are the only two consecutive perfect powers of natural numbers – in 1844 in a letter to the editor of Crelle’s mathematical journal. One hundred and fifty-eight years later, Preda Mihailescu proved it. Catalan’s Conjecture presents thi...

Πίνακας περιεχομένων:

• The Case “q = 2”
• The Case “p = 2”
• The Nontrivial Solution
• Runge’s Method
• Cassels’ theorem
• An Obstruction Group
• Small p or q
• The Stickelberger Ideal
• The Double Wieferich Criterion
• The Minus Argument
• The Plus Argument I
• Semisimple Group Rings
• The Plus Argument II
• The Density Theorem
• Thaine’s Theorem.