Periodical:

The Bulletin of Society for Mathematical Services and Standards (Volume 7)

Pages:

23-39

Citation:

K. Zelator "Integer Solutions, Rational Solutions of the Equations x^{4}+y^{4}+z^{4}-2x^{2}y^{2}-2y^{2}z^{2}-2z^{2}x^{2}=n and x^{2}+y^{4}+z^{4}-2xy^{2}-2xz^{2}-2y^{2}z^{2}=n - And Crux Mathematicorum Contest Corner Problem CC24", The Bulletin of Society for Mathematical Services and Standards, Vol. 7, pp. 23-39, 2013

Online since:

September 2013

Authors:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

Crux Mathematicorum, No 5 (May 2013), Vol 38, Contest Corner problem CC24, page 174 Given the equation, x4 y 4 z 4 2 y 2 z 2 2z 2 x2 2 x2 y 2 24 (a) Prove that the equation has no integer solutions (b) Does this equation have rational solutions? If yes, give an example. If no, prove it.

W. Sierpinski, Elementary Theory of Numbers, Warsaw 1964, 480pp. ISBN: 0-598-52758-3 For the result that states that is a natural number is the mth power of rational number, and m is natural; see Theorem 7, on page 16 For the Pythagorean equation x2 y 2 z 2 , see pages 3842.

Konstantine Zelator, The Diophantine equation x2 ky2 z 2 , and Integral Triangles with a Cosine Value of Mathematics and Computer Education Vol 30, No 3, pp.191-197, Fall (2006).