cp's OEIS Frontend

A235383 Fibonacci numbers that are the product of other Fibonacci numbers.

%I A235383 #45 Jun 28 2025 16:11:18
%S A235383 8,144
%N A235383 Fibonacci numbers that are the product of other Fibonacci numbers.
%C A235383 This sequence and A229037 and A235265 are winners in the contest held at the 2014 AMS/MAA Joint Mathematics Meetings. - _T. D. Noe_, Jan 20 2014
%C A235383 Carmichael's theorem implies that 8 and 144 are the only terms of this sequence.
%C A235383 First two terms of A061899, A111687, A172150, A212703, and A231851. - _Omar E. Pol_, Jan 21 2014
%C A235383 Saha and Karthik conjectured (without reference to Carmichael's theorem) that the only positive integers k for which A001175(k^2) = A001175(k) are 6 and 12. (A000045(6) = 8 and A000045(12) = 144.) - _L. Edson Jeffery_, Feb 13 2014
%C A235383 Y. Bugeaud, M. Mignotte, and S. Siksek proved that 8 and 144 are the only nontrivial perfect power Fibonacci numbers. - _Robert C. Lyons_, Dec 23 2015
%H A235383 Yann Bugeaud, Maurice Mignotte, and Samir Siksek, <a href="http://annals.math.princeton.edu/wp-content/uploads/annals-v163-n3-p05.pdf">Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers</a>, Annals of Mathematics, 163 (2006), pp. 969-1018.
%H A235383 Arpan Saha and Karthik C S, <a href="http://arxiv.org/abs/1102.1636">A few equivalences of Wall-Sun-Sun prime conjecture</a>, arXiv:1102.1636 [math.NT], 2011.
%H A235383 Wikipedia, <a href="http://en.wikipedia.org/wiki/Carmichael%27s_theorem">Carmichael's theorem</a>.
%e A235383 The Fibonacci number 8 is in the sequence because 8=2*2*2, and 2 is a Fibonacci number that is not equal to 8. The Fibonacci number 144 is in the sequence because 144=3*3*2*2*2*2, and both 2 and 3 are Fibonacci numbers that are not equal to 144.
%Y A235383 Cf. A000045, A061899, A065108, A227875.
%K A235383 nonn,bref,fini,full,nice
%O A235383 1,1
%A A235383 _Robert C. Lyons_, Jan 08 2014