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.
%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
}