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A206786
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Remainder of n^340 divided by 341.
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1
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1, 1, 56, 1, 67, 56, 56, 1, 67, 67, 253, 56, 67, 56, 1, 1, 56, 67, 56, 67, 67, 253, 1, 56, 56, 67, 1, 56, 1, 1, 155, 1, 187, 56, 1, 67, 56, 56, 1, 67, 67, 67, 56, 253, 56, 1, 1, 56, 67, 56, 67, 67, 67, 1, 242, 56, 67, 1, 56, 1, 1, 155, 1, 1, 56, 187, 67
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OFFSET
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1,3
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COMMENTS
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The n for which a(n) = 1 indicate the bases to which 341 is a Fermat pseudoprime. 341 is the smallest base 2 Fermat pseudoprime.
The only a(n) that occur are 0, 1, 56, 67, 155, 187, 242, 253. If n is one of these eight numbers, then a(n) = n.
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REFERENCES
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David Wells, Prime Numbers: The Most Mysterious Figures in Math. Hoboken, New Jersey: John Wiley & Sons (2005): 191
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LINKS
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EXAMPLE
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a(2) = 1 because 2^340/341 leaves a remainder of 1 (the prime factors of 2^340 - 1 include 11 and 31).
a(3) = 56 because 3^340/341 leaves a remainder of 56 (the prime factors of 3^340 - 56 are 5, 11, 31 and a prime number with more than a hundred digits).
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MATHEMATICA
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Table[Mod[n^340, 341], {n, 100}]
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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