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EISENSTEIN-JACOBI INTEGER SOLUTIONS FOR THE FIFTH POWER TAXICAB NUMBER PROBLEM
Keywords:
taxicab number problem, Eisenstein-Jacobi integers, Gaussian integers, Diophantine higher degree equationDOI:
https://doi.org/10.17654/0972555522027Abstract
The famous open problem of finding positive integer solutions to $a^5+b^5=c^5+d^5$ is considered, and related solutions are found in the ring of Eisenstein-Jacobi integers.
Received: June 2, 2022
Accepted: July 9, 2022
References
G. B. Campbell and A. Zujev, Gaussian integer solutions for the fifth power taxicab number problem. arXiv:1511.07424v1.
L. E. Dickson, History of the Theory of Numbers, Vol. II, Ch. XXII, P. 644, Originally published 1919 by Carnegie Inst of Washington, Reprinted by The American Mathematical Society, 1999.
G. H. Hardy, Ramanujan, Cambridge University Press, 1927.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 3rd ed., Oxford University Press, London and NY, 1954.
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