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Procedures are given for evaluation of modulo m exponential towers of powers, or exponents upon exponents upon exponents ad infinitum. Sufficient conditions are given to analyze any tower including an infinite tower. Applications are made to binary exponentiation and exponentiation in the finite ring Zm. Sample problems include finding last digits, finding a natural number that does not divide, finding an integer and showing a sequence is constant for any base.

Attempts are made to generalize Poisson's method by multiplying more copies of the original definite integral to obtain a triple or quadruple integral that can be evaluated using spherical polar coordinates. The trick has only one application, which is important to mathematics and statistics.

Byline: Robert J. MacG. Dawson (1) Author Affiliation: (1) Department of Mathematics & Computing Science, St. Mary's University, Halifax, NS, B3H 3C3, Canada Article History: Registration Date: 17/11/2008 Received Date: 16/10/2008 Accepted Date: 17/11/2008 Online Date: 12/02/2009

Byline: Robert J. MacG. Dawson (1) Author Affiliation: (1) Department of Mathematics & Computer Science, St. Mary's University, Halifax, NS, B3H 3C3, Canada Article History: Registration Date: 02/11/2009 Online Date: 13/01/2010

Byline: Robert J. MacG. Dawson (1) Author Affiliation: (1) Department of Mathematics & Computing Science, St. Mary's University, Halifax, NS B3H 3C3, Canada Article History: Registration Date: 17/11/2008 Received Date: 27/10/2008 Accepted Date: 17/11/2008 Online Date: 13/02/2009