A206786 Remainder of n^340 divided by 341.
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
Examples
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).
References
- David Wells, Prime Numbers: The Most Mysterious Figures in Math. Hoboken, New Jersey: John Wiley & Sons (2005): 191
Links
Programs
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Mathematica
Table[Mod[n^340, 341], {n, 100}] PowerMod[Range[80],340,341] (* Harvey P. Dale, Jun 04 2017 *) -
PARI
a(n)=lift(Mod(n,341)^340) \\ Charles R Greathouse IV, May 01 2012
Comments