Ajai Choudhry
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 21, 2015, Number 4, Pages 1—5
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Ajai Choudhry
13/4 A Clay Square,
Lucknow, India
Abstract
This paper is concerned with integer solutions of the diophantine equation x_{1}^{4} + x_{2}^{4} + x_{3}^{4} = k x_{4}^{2} where k is a given positive integer. Till now, integer and parametric solutions of this diophantine equation have been published only when k = 1 or 2 or 3. In this paper we obtain parametric solutions of this equation for 43 values of k ≤ 100. We also show that the equation cannot have any solution in integers for 54 values of k ≤ 100. The solvability of the equation x_{1}^{4} + x_{2}^{4} + x_{3}^{4} = k x_{4}^{2} where k could not be determined for three values of k ≤ 100, namely 34, 35 and 65.
Keywords
- Biquadrates
- Sums of biquadrates
AMS Classification
- 11D25
References
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Cite this paper
APAChoudhry, A. (2015). Some Diophantine equations concerning biquadrates. Notes on Number Theory and Discrete Mathematics, 21(4), 1-5.
ChicagoChoudhry, Ajai. “Some Diophantine Equations concerning Biquadrates.” Notes on Number Theory and Discrete Mathematics 21, no. 4 (2015): 1-5.
MLAChoudhry, Ajai. “Some Diophantine Equations concerning Biquadrates.” Notes on Number Theory and Discrete Mathematics 21.4 (2015): 1-5. Print.