Limits RegistryPUBLIC RECORD
Limits RegistryPreda Mihailescu proved Catalan's Conjecture, first stated by Eugène Charles Catalan in 1844, in a 2002 paper published in Crelle's Journal in 2004. The proof uses techniques from the theory of cyclotomic fields, in particular results about Wieferich pairs, and settled a problem that had resisted attack for over 150 years despite earlier partial results by Cassels and others.
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Preda Mihailescu proved Catalan's Conjecture, first stated by Eugène Charles Catalan in 1844, in a 2002 paper published in Crelle's Journal in 2004. The proof uses techniques from the theory of cyclotomic fields, in particular results about Wieferich pairs, and settled a problem that had resisted attack for over 150 years despite earlier partial results by Cassels and others.
The only solution in the natural numbers of x^p - y^q = 1 for x, y, p, q all greater than 1 is 3^2 - 2^3 = 1, i.e. 8 and 9 are the only consecutive perfect powers.
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Permanent ID limitsregistry.com/limits/LR-CATALANS-CONJECTURE
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Limits Registry. LR-CATALANS-CONJECTURE. Proof of Catalan's Conjecture (Mihailescu's Theorem). 2026.