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A227875
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Fibonacci numbers which are perfect powers.
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6
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OFFSET
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1,3
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COMMENTS
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Also, Fibonacci numbers which are products of Fibonacci numbers (each greater than 1 when the product is greater than 1 - see A235383). - Rick L. Shepherd, Feb 19 2014
The terms of the subsequence (1, 8, 144) are the Fibonacci numbers that are powerful numbers. - Robert C. Lyons, Jul 12 2016
Also Fibonacci numbers without any primitive divisors. See [Heuberger & Wagner]. - Michel Marcus, Aug 21 2016
It was proved (Bugeaud, Mignotte, and Siksek, 2006, p. 971) that the only perfect powers among the Fibonacci numbers and Lucas numbers are {0, 1, 8, 144} and {1, 4}, respectively. - Daniel Forgues, Apr 09 2018
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LINKS
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Vladica Andrejic, On Fibonacci Powers, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 17 (2006), 38-44.
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MATHEMATICA
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perfectPowerQ[0] = True; perfectPowerQ[1] = True; perfectPowerQ[n_] := GCD @@ FactorInteger[n][[All, 2]] > 1; Union[Select[Fibonacci /@ Range[0, 20], perfectPowerQ]]
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CROSSREFS
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KEYWORD
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nonn,bref,fini,full
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AUTHOR
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STATUS
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approved
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