Triples of sixth powers with equal sums
Author:
Simcha Brudno
Journal:
Math. Comp. 30 (1976), 646648
MSC:
Primary 10B15
MathSciNet review:
0406923
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Abstract: The diophantine equation is shown to have a twoparameter solution which is homogeneous of degree four. The solution also satisfies ; and in addition, .
 [1]
Simcha
Brudno, On generating infinitely many
solutions of the Diophantine equation
𝐴⁶+𝐵⁶+𝐶⁶=𝐷⁶+𝐸⁶+𝐹⁶,
Math. Comp. 24 (1970), 453–454. MR 0271020
(42 #5903), http://dx.doi.org/10.1090/S00255718197002710204
 [2]
Simcha
Brudno and Irving
Kaplansky, Equal sums of sixth powers, J. Number Theory
6 (1974), 401–403. MR 0371809
(51 #8026)
 [3]
G.
H. Hardy and E.
M. Wright, An introduction to the theory of numbers, Oxford,
at the Clarendon Press, 1954. 3rd ed. MR 0067125
(16,673c)
 [4]
L.
J. Lander, T.
R. Parkin, and J.
L. Selfridge, A survey of equal sums of like
powers, Math. Comp. 21 (1967), 446–459. MR 0222008
(36 #5060), http://dx.doi.org/10.1090/S00255718196702220080
 [5]
K. SUBBA RAO, "On sums of sixth powers," J. London Math. Soc., v. 9, 1934, pp. 172173.
 [1]
 SIMCHA BRUDNO, "On generating infinitely many solutions of the Diophantine equation ," Math. Comp, v. 24, 1970, pp. 453454. MR 42 #5903. MR 0271020 (42:5903)
 [2]
 SIMCHA BRUDNO & IRVING KAPLANSKY, "Equal sums of sixth powers," J. Number Theory, v. 6, 1974, pp. 401403. MR 0371809 (51:8026)
 [3]
 G. H. HARDY & E. M. WRIGHT, An Introduction to the Theory of Numbers, 3rd ed., Clarendon Press, Oxford, 1954, Chapter 21 (the comment is dropped in the 4th ed.). MR 16, 673. MR 0067125 (16:673c)
 [4]
 L. J. LANDER, T. R. PARKIN & J. L. SELFRIDGE, "A survey of equal sums of like powers," Math. Comp., v. 21, 1967, pp. 446459. MR 36 #5060. MR 0222008 (36:5060)
 [5]
 K. SUBBA RAO, "On sums of sixth powers," J. London Math. Soc., v. 9, 1934, pp. 172173.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197604069236
PII:
S 00255718(1976)04069236
Article copyright:
© Copyright 1976
American Mathematical Society
