A125258 - OEIS

A125258

Smallest prime divisor of n^4-n^2+1.

13, 73, 241, 601, 13, 13, 37, 6481, 9901, 13, 20593, 28393, 37, 13, 97, 83233, 229, 13, 13, 61, 157, 37, 13, 390001, 181, 530713, 13, 37, 809101, 922561, 13, 13, 1069, 277, 1678321, 13, 2083693, 2311921, 61, 13, 673, 3416953, 1753, 13, 13, 1213, 5306113

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,1

COMMENTS

All divisors of n^4-n^2+1 are congruent to 1 modulo 12.

a(n) = 13 if and only if n is congruent to 2, -2, 6, or -6 modulo 13.

REFERENCES

K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, NY, Second Edition (1990), p. 63.

LINKS

Nick Hobson, Table of n, a(n) for n = 2..1000

EXAMPLE

The prime divisors of 6^4-6^2+1=1261 are 13 and 97, so a(5) = 13.