Ajai Choudhry

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 24, 2018, Number 2, Pages 140—144

DOI: 10.7546/nntdm.2018.24.2.140-144

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## Details

### Authors and affiliations

Ajai Choudhry

*13/4 A Clay Square, Lucknow – 226001, India
*

### Abstract

This paper is concerned with the Diophantine equation

_{i=1}

^{n}

*a*

_{i}x_{i}^{4}= ∑

_{i=1}

^{n}

*a*

_{i}y_{i}^{4},

*n*≥ 3 and

*a*,

_{i}*i*= 1, 2, …,

*n*, are arbitrary nonzero integers. While a method of obtaining numerical solutions of such an equation has recently been given, it seems that an explicit parametric solution of this Diophantine equation has not yet been published. We obtain a multi-parameter solution of this equation for arbitrary values of

*a*and for any positive integer

_{i}*n*≥ 3, and deduce specific solutions when

*n*= 3 and

*n*= 4. The numerical solutions thus obtained are much smaller than the integer solutions of such equations obtained earlier.

### Keywords

- Biquadrates
- Fourth powers
- Quartic Diophantine equation

### 2010 Mathematics Subject Classification

- 11D25

### References

- Choudhry, A. (1991) Symmetric Diophantine systems, Acta Arithmetica, 59, 291–307.
- Choudhry, A. (2013) Equal sums of like powers and equal products of integers, Rocky Mountain Journal of Mathematics, 43, 763–792
- Dickson, L. E. (1992) History of theory of numbers, Vol. 2, Chelsea Publishing Company, New York.
- Izadi, F., & Baghalaghdam, M. (2017) On the Diophantine equation ∑
_{i=1}^{n}*a*_{i}x_{i}^{4}= ∑_{j=1}^{n}*a*_{j}y_{j}^{4}, available at arXiv:1701.02605.

## Related papers

## Cite this paper

APAChoudhry, A. (2018). A symmetric Diophantine equation involving biquadrates. Notes on Number Theory and Discrete Mathematics, 24(2), 140-144, doi: 10.7546/nntdm.2018.24.2.140-144.

ChicagoChoudhry, Ajai. “A Symmetric Diophantine Equation Involving Biquadrates.” Notes on Number Theory and Discrete Mathematics 24, no. 2 (2018): 140-144, doi: 10.7546/nntdm.2018.24.2.140-144.

MLAChoudhry, Ajai. “A Symmetric Diophantine Equation Involving Biquadrates.” Notes on Number Theory and Discrete Mathematics 24.2 (2018): 140-144. Print, doi: 10.7546/nntdm.2018.24.2.140-144.