Catalan,s Diophantine Problem
المؤلف:
Inkeri, K.
المصدر:
"On Catalan,s Problem." Acta Arith. 9
الجزء والصفحة:
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16-5-2020
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Catalan's Diophantine Problem
Find consecutive powers, i.e., solutions to
excluding 0 and 1. Catalan's conjecture states that the only solution is 
, so 8 and 9 (
and 
) are the only consecutive powers (again excluding 0 and 1).
REFERENCES:
Cassels, J. W. S. "On the Equation 
. II." Proc. Cambridge Phil. Soc. 56, 97-103, 1960.
Inkeri, K. "On Catalan's Problem." Acta Arith. 9, 285-290, 1964.
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