Search: id:A002760
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%I A002760
%S A002760 0,1,4,8,9,16,25,27,36,49,64,81,100,121,125,144,169,196,216,
%T A002760 225,256,289,324,343,361,400,441,484,512,529,576,625,676,
%U A002760 729,784,841,900,961,1000,1024,1089,1156,1225,1296,1331
%N A002760 Squares and cubes.
%C A002760 Catalan's Conjecture states that 8 and 9 are the only pair of consecutive 
               numbers in this sequence. The conjecture was established in 2003 
               by Mihilescu.
%D A002760 Bilu, Y. F., Catalan's Conjecture (After Mihilescu). Asterisque, No. 
               294, 1-26, 2004.
%D A002760 Bilu, Y. F., Catalan Without Logarithmic Forms (after Bugeaud, Hanrot 
               and Mihilescu). J. Theor. Nombres Bordeaux 17, 69-85, 2005.
%D A002760 Metsankyla, T., Catalan's Conjecture: Another Old Diophantine Problem 
               Solved. Bull. Amer. Math. Soc. 41, 43-57, 2003.
%D A002760 Mihilescu, P., A Class Number Free Criterion for Catalan's Conjecture. 
               J. Number Th. 99 225-231, 2003.
%D A002760 Mihilescu, P., Primary Cyclotomic Units and a Proof of Catalan's Conjecture. 
               J. Reine Angew. Math. 572, 167-195, 2004.
%D A002760 P. Ribenboim, Catalan's conjecture, Amer. Math. Monthly, 103 (1996), 
               529-538.
%D A002760 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 
               68.
%D A002760 C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 236.
%H A002760 Zak Seidov, <a href="b002760.txt">Table of n, a(n) for n = 1..1000.</
               a>
%Y A002760 Cf. A131799; union of A000290 and A000578.
%Y A002760 Sequence in context: A134612 A025475 A125643 this_sequence A115651 A062559 
               A010417
%Y A002760 Adjacent sequences: A002757 A002758 A002759 this_sequence A002761 A002762 
               A002763
%K A002760 nonn
%O A002760 1,3
%A A002760 N. J. A. Sloane (njas(AT)research.att.com).

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