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A212423
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Frobenius pseudoprimes == 2,3 (mod 5) with respect to Fibonacci polynomial x^2 - x - 1.
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3
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5777, 10877, 75077, 100127, 113573, 161027, 162133, 231703, 430127, 635627, 851927, 1033997, 1106327, 1256293, 1388903, 1697183, 2263127, 2435423, 2662277, 3175883, 3399527, 3452147, 3774377, 3900797, 4109363, 4226777, 4403027, 4828277, 4870847
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OFFSET
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1,1
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COMMENTS
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Grantham incorrectly claims that "the first Frobenius pseudoprime with respect to the Fibonacci polynomial x^2 - x - 1 is 5777". However n = 5777 is the first Frobenius pseudoprime with respect to x^2 - x - 1 that has Jacobi symbol (5/n) = -1, i.e., n == 2,3 (mod 5). Unrestricted version with the first term 4181 is given in A212424.
Composite k == 2,3 (mod 5) such that Fibonacci(k) == -1 (mod k) and that k divides Fibonacci(k+1). - Jianing Song, Sep 12 2018
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REFERENCES
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R. Crandall, C. B. Pomerance. Prime Numbers: A Computational Perspective. Springer, 2nd ed., 2005.
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LINKS
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PROG
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(PARI) { isFP23(n) = if(ispseudoprime(n), return(0)); t=Mod(x*Mod(1, n), (x^2-x-1)*Mod(1, n))^n; (kronecker(5, n)==-1 && t==1-x) }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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