A270827 a(n) is the smallest k such that k^8 = 16 (mod 2*n-1).

1, 1, 1, 3, 4, 3, 4, 1, 3, 6, 4, 5, 6, 5, 11, 8, 8, 3, 5, 4, 8, 16, 4, 7, 10, 5, 22, 3, 13, 23, 10, 4, 4, 20, 5, 12, 12, 8, 3, 9, 22, 9, 3, 11, 25, 4, 8, 6, 14, 14, 9, 38, 4, 31, 32, 5, 14, 18, 4, 3, 19, 8, 56, 16, 16, 28, 25, 22, 31, 50, 7, 19, 11, 10, 43, 46, 5

Offset

1,4

Comments

Motivated by Crandall & Pomerance, Exercise 2.1 p. 108: "Prove that 16 is, modulo any odd number, an eighth power".

References

R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see Exercise 2.1 p. 108.

Links

Table of n, a(n) for n=1..77.

Example

a(9)=3 since for odd number 2*9-1=17, 3^8 = 16 (mod 17).

Mathematica

Table[SelectFirst[Range@ 1000, Mod[#^8, 2 n - 1] == Mod[16, 2 n - 1] &], {n, 77}] (* Michael De Vlieger, Mar 24 2016, Version 10 *)

Prog

(PARI) a(n) = { my(m = 2*n-1, k = 1); while(Mod(k, m)^8 != 16, k++); k; }

Crossrefs

Sequence in context: A094237 A016654 A090673 * A293072 A120447 A083021

Adjacent sequences: A270824 A270825 A270826 * A270828 A270829 A270830

Keyword

nonn

Author

Michel Marcus, Mar 23 2016

Status

approved