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A206786
Remainder of n^340 divided by 341.
2
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
OFFSET
1,3
COMMENTS
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.
Periodic with period 341. - Charles R Greathouse IV, May 01 2012
REFERENCES
David Wells, Prime Numbers: The Most Mysterious Figures in Math. Hoboken, New Jersey: John Wiley & Sons, 2005, p. 191.
EXAMPLE
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).
MATHEMATICA
Table[Mod[n^340, 341], {n, 100}]
PowerMod[Range[80], 340, 341] (* Harvey P. Dale, Jun 04 2017 *)
PROG
(PARI) a(n)=lift(Mod(n, 341)^340) \\ Charles R Greathouse IV, May 01 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alonso del Arte, Feb 12 2012
STATUS
approved