%0 Generic %1 citeulike:3036284 %A Euler, Leonhard %D 2005 %K Vor1800 available-in-tex-format mathematics number-theory pre1800 %T Observations about two biquadratics, of which the sum is able to be resolved into two other biquadratics %U http://arxiv.org/abs/math/0505629 %X In this paper Euler considers the Diophantine equation A^4+B^4=C^4+D^4. He gives a method for finding solutions of it, and gives two particular solutions of A=2219449, B=-555617, C=1584749, D=2061283 and A=477069, B=8497, C=310319, D=428397; the first four satisfy this but the second four do not. Euler also states the ``Euler quartic conjecture'' in this paper, that there is no biquadratic which is the sum of three other biquadratics. However, this may be because of typographical errors or a bad digital copy of the original, and I will try to get a cleaner copy to double check.

@misc{citeulike:3036284, abstract = {In this paper Euler considers the Diophantine equation A^4+B^4=C^4+D^4. He gives a method for finding solutions of it, and gives two particular solutions of A=2219449, B=-555617, C=1584749, D=2061283 and A=477069, B=8497, C=310319, D=428397; the first four satisfy this but the second four do not. Euler also states the ``Euler quartic conjecture'' in this paper, that there is no biquadratic which is the sum of three other biquadratics. However, this may be because of typographical errors or a bad digital copy of the original, and I will try to get a cleaner copy to double check.}, added-at = {2009-08-02T17:14:35.000+0200}, archiveprefix = {arXiv}, author = {Euler, Leonhard}, biburl = {https://www.bibsonomy.org/bibtex/217d992c8ccdd9b3004f7e3749a7f2b1d/rwst}, citeulike-article-id = {3036284}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0505629}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0505629}, description = {my bookmarks from citeulike}, eprint = {math/0505629}, interhash = {ca0fb264efa84c94c44ae34bce2e0147}, intrahash = {17d992c8ccdd9b3004f7e3749a7f2b1d}, keywords = {Vor1800 available-in-tex-format mathematics number-theory pre1800}, month = May, posted-at = {2008-07-23 08:49:05}, priority = {2}, timestamp = {2009-08-06T10:25:20.000+0200}, title = {Observations about two biquadratics, of which the sum is able to be resolved into two other biquadratics}, url = {http://arxiv.org/abs/math/0505629}, year = 2005 }