A Polynomial or polynomial equation is said to be irreducible if it cannot be factored into polynomials of lower degree over the same Field.

The number of binary irreducible polynomials of degree is equal to the number of -bead fixed Necklaces of two colors: 1, 2, 3, 4, 6, 8, 14, 20, 36, ... (Sloane's A000031), the first few of which are given in the following table.

Polynomials | |

1 | |

2 | , |

3 | , , |

4 | , , , |

**References**

Sloane, N. J. A. Sequence
A000031/M0564
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and extended entry in
Sloane, N. J. A. and Plouffe, S.
*The Encyclopedia of Integer Sequences.* San Diego: Academic Press, 1995.

© 1996-9

1999-05-26