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On the class groups of cyclotomic extensions in presence of a solution to Catalan's equation

✍ Scribed by Preda Mihăilescu

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
209 KB
Volume
118
Category
Article
ISSN
0022-314X

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✦ Synopsis

Catalan's conjecture states that the equation x py q = 1 has no other integer solutions but 3 2 -2 3 = 1. We investigate the consequences of existence of further solutions (with odd prime exponents p, q) upon the relative class group of the pth cyclotomic extension. We thus obtain several new results which merge into the condition q ≡ 1 mod p and p ≡ 1 mod q.

This condition is used in the proof of Catalan's conjecture.

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