Mathematics of Computation

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Equal sums of four seventh powers

Author(s): Randy L. Ekl.
Journal: Math. Comp. 65 (1996), 1755-1756.
MSC (1991): Primary 11D41, 11Y50; Secondary 11P05
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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.

References:

[1]: Richard K. Guy, Unsolved Problems in Number Theory, Second Edition, Springer-Verlag, New York, 1994. CMP 95:02
[2]: Ellis Horowitz and Sartaj Sahni, Fundamentals of Data Structures, Computer Science Press, Inc., Potomac, MD, 1976. MR 54:6540
[3]: G. H. Hardy and E. M. Wright, Introduction to the Theory of Numbers, 5th edition, Oxford University Press, New York, 1980. MR 81i:10002
[4]: L. J. Lander, T. R. Parkin and J. L. Selfridge, A Survey of Equal Sums of Like Powers, Mathematics of Computation 21 (1967), 446--459. MR 36:5060


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