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Mathematics of Computation

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Equal sums of four seventh powers

Author: Randy L. Ekl
Journal: Math. Comp. 65 (1996), 1755-1756
MSC (1991): Primary 11D41, 11Y50; Secondary 11P05
MathSciNet review: 1361807
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Abstract: In this paper, the method used to find the smallest, nontrivial, positive integer solution of $a_1^7+a_2^7+a_3^7+a_4^7=b_1^7+b_2^7+b_3^7+b_4^7$ is discussed. The solution is

\begin{equation*}149^7+123^7+14^7+10^7= 146^7+129^7+90^7+15^7.\end{equation*}

Factors enabling this discovery are advances in computing power, available workstation memory, and the appropriate choice of optimized algorithms.

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Additional Information

Randy L. Ekl
Affiliation: 930 Lancaster Lane, Lake Zurich, Illinois 60047

Keywords: Diophantine equation, number theory
Received by editor(s): May 10, 1995
Received by editor(s) in revised form: July 5, 1995, and September 7, 1995
Article copyright: © Copyright 1996 American Mathematical Society