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Search: id:A125258
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| A125258 |
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Smallest prime divisor of n^4-n^2+1. |
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+0
1
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| 13, 73, 241, 601, 13, 13, 37, 6481, 9901, 13, 20593, 28393, 37, 13, 97, 83233, 229, 13, 13, 61, 157, 37, 13, 390001, 181, 530713, 13, 37, 809101, 922561, 13, 13, 1069, 277, 1678321, 13, 2083693, 2311921, 61, 13, 673, 3416953, 1753, 13, 13, 1213, 5306113
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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All divisors of n^4-n^2+1 are congruent to 1 modulo 12.
a(n) = 13 if and only if n is congruent to 2, -2, 6, or -6 modulo 13.
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REFERENCES
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K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, NY, Second Edition (1990), p. 63.
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LINKS
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N. Hobson, Table of n, a(n) for n = 2..1000
N. Hobson, Home page (listed in lieu of email address)
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EXAMPLE
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The prime divisors of 6^4-6^2+1=1261 are 13 and 97, so a(5) = 13.
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PROGRAM
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(PARI) vector(49, n, if(n<2, "-", factor(n^4-n^2+1)[1, 1]))
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CROSSREFS
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Cf. A060886, A124990.
Sequence in context: A139873 A142787 A084218 this_sequence A060886 A081586 A143008
Adjacent sequences: A125255 A125256 A125257 this_sequence A125259 A125260 A125261
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KEYWORD
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easy,nonn
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AUTHOR
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Nick Hobson Nov 26 2006
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