A270827 - OEIS

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

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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