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A319168
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Frobenius pseudoprimes == 1,4 (mod 5) with respect to Fibonacci polynomial x^2 - x - 1.
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1
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4181, 6721, 13201, 15251, 34561, 51841, 64079, 64681, 67861, 68251, 90061, 96049, 97921, 118441, 146611, 163081, 186961, 197209, 219781, 252601, 254321, 257761, 268801, 272611, 283361, 302101, 303101, 330929, 399001, 433621, 438751, 489601, 512461, 520801
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OFFSET
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1,1
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COMMENTS
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Composite k == 1,4 (mod 5) such that Fibonacci(k) == 1 (mod k) and that k divides Fibonacci(k-1).
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LINKS
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Jon Grantham, Frobenius pseudoprimes, Mathematics of Computation 70 (234): 873-891, 2001. doi: 10.1090/S0025-5718-00-01197-2.
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EXAMPLE
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4181 = 37*113 is composite, while Fibonacci(4180) == 0 (mod 4181), Fibonacci(4181) == 1 (mod 4181), so 4181 is a term.
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PROG
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(PARI) for(n=2, 500000, if(!isprime(n) && (n%5==1||n%5==4) && fibonacci(n-kronecker(5, n))%n==0 && (fibonacci(n)-kronecker(5, n))%n==0, print1(n, ", ")))
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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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