*N.B. A detailed on-line essay by S. Finch
was the starting point for this entry.*

Given two randomly chosen Integer matrices, what is the probability that the corresponding
determinants are coprime? Hafner *et al. *(1993) showed that

(1) |

(2) |

(3) |

**References**

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/hafner/hafner.html

Flajolet, P. and Vardi, I. ``Zeta Function Expansions of Classical Constants.'' Unpublished manuscript. 1996. http://pauillac.inria.fr/algo/flajolet/Publications/landau.ps.

Hafner, J. L.; Sarnak, P.; and McCurley, K. ``Relatively Prime Values of Polynomials.'' In *Contemporary Mathematics*
Vol. 143 (Ed. M. Knopp and M. Seingorn). Providence, RI: Amer. Math. Soc., 1993.

Vardi, I. *Computational Recreations in Mathematica.* Redwood City, CA: Addison-Wesley, 1991.

© 1996-9

1999-05-25