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Class number bounds and Catalan's equation |
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| Authors: | Ray Steiner. |
| Affiliation: | Department of Mathematics, Bowling Green State University, Bowling Green, Ohio 43403 |
| Abstract: | We improve a criterion of Inkeri and show that if there is a solution to Catalan's equation
with |
| Keywords: | Catalan's equation class number bounds algebraic number fields |
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and 
prime numbers greater than 3 and both congruent to 3 
, then 
and 
form a double Wieferich pair. Further, we refine a result of Schwarz to obtain similar criteria when only one of the exponents is congruent to 3 
. Indeed, in light of the results proved here it is reasonable to suppose that if 
, then 
and 
form a double Wieferich pair.