A class number free criterion for catalan's conjecture |
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| Authors: | Preda Mihǎilescu |
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| Affiliation: | Mathematik Abteilung, Uni-Paderborn, Warburgerstr. 100, Paderborn DE-33095, Germany |
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| Abstract: | The Catalan conjecture asserts that the equation XU−YV=1 with U,V>1 has no other solution in integers but 32−23=1 (Catalan's Conjecture, Academic Press, New York, 1994). We prove that, for primes U=p and V=q yielding a solution to the Catalan equation, the simultaneous conditions |
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