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On the Diophantine equation $a^{3}+b^{3}+c^{3}+d^{3}=0$. (English) Zbl 1031.11015
The equation in the title has been studied by many mathematicians since Diophantus. Partial solutions in integers and complete solutions in rational numbers have been found. The main result shows how “every integral primitive solution $(a,b,c,d)$ can be written uniquely”.
MSC:
11D25Cubic and quartic diophantine equations
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References:
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[2] Choudhry, A.: On equal sums of cubes. Rocky mountain J. Math. 28, 1251-1257 (1998) · Zbl 0934.11011
[3] Dickson, L. E.: History of the theory of numbers, vol. 2, Diophantine analysis. (1966) · Zbl 0958.11500
[4] Hua, L. -K.: Introduction to number theory. (1982)
[5] Hardy, G. H.; Wright, E. M.: An introduction to the theory of numbers. (1979) · Zbl 0423.10001
[6] B. C. Berndt, (Ed.), Ramanujan’s Notebooks, Springer-Verlag, New York, 1985--1998. · Zbl 0389.10002
[7] Sándor, C.: On the equation a3+b3+c3=d3. Period. math. Hungar. 33, 121-134 (1996)