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A090968
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Primes p such that p^2 divides 19^(p-1) - 1.
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5
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OFFSET
| 1,1
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COMMENTS
| Primes p such that p divides the Fermat quotient of p (with base 19). The Fermat quotient of p with base a denotes the integer q_p(a) = ( a^(p-1) - 1) / p, where p is a prime which does not divide the integer a. - C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 20 2005
No further terms up to 3.127*10^13.
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REFERENCES
| J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 43, p. 17, Ellipses, Paris 2008.
Paulo Ribenboim, "The Little Book Of Big Primes," Springer-Verlag, NY 1991, page 170.
Roozbeh Hazrat, Mathematica:A Problem-Centered Approach, Springer 2010, pp. 39, 171
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LINKS
| C. Caldwell, Fermat quotient
W. Keller and J. Richstein Fermat quotients q_p(a) that are divisible by p
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MATHEMATICA
| NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ p = NextPrim[p]; If[PowerMod[19, p - 1, p^2] == 1, Print[p]], {n, 1, 2*10^8}]
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CROSSREFS
| Cf. A001220, A014127, A123692, A123693, A128667, A128668, A128669, A039951, A096082
Sequence in context: A191974 A174241 A086208 * A020641 A062736 A103564
Adjacent sequences: A090965 A090966 A090967 * A090969 A090970 A090971
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KEYWORD
| nonn,hard,more
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 27 2004
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EXTENSIONS
| Third reference added by Harvey P. Dale, Oct. 17 2011
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