A practical algorithm for determining if there exist integers for given real numbers such that

or else establish bounds within which no such Integer Relation can exist (Ferguson and Forcade 1979). A nonrecursive variant of the original algorithm was subsequently devised by Ferguson (1987). The Ferguson-Forcade algorithm has shown that there are no algebraic equations of degree with integer coefficients having Euclidean norms below certain bounds for , , , , , , , and , where

Constant | Bound |

**References**

Bailey, D. H. ``Numerical Results on the Transcendence of Constants Involving , , and Euler's Constant.''
*Math. Comput.* **50**, 275-281, 1988.

Ferguson, H. R. P. ``A Short Proof of the Existence of Vector Euclidean Algorithms.'' *Proc. Amer. Math. Soc.* **97**, 8-10, 1986.

Ferguson, H. R. P. ``A Non-Inductive GL() Algorithm that Constructs Linear Relations for -Linearly Dependent Real Numbers.''
*J. Algorithms* **8**, 131-145, 1987.

Ferguson, H. R. P. and Forcade, R. W. ``Generalization of the Euclidean Algorithm for Real Numbers to All Dimensions Higher than Two.''
*Bull. Amer. Math. Soc.* **1**, 912-914, 1979.

© 1996-9

1999-05-26