An algebraic problem of finding four numbers, given the products of each of the numbers with the sum of the three others Export

@misc{citeulike:3036294, abstract = {In this paper Euler considers the problem of given a,b,c,d where a=v(x+y+z), b=x(v+y+z), c=y(v+x+z), d=z(v+x+y), determining v,x,y,z. He makes many changes of variable and ends up with four nicer equations, each in terms of a new variable u and the constants a,b,c,d. I do not understand exactly what Euler is doing, but I think the translation is ``correct''. If anyone understands what Euler is doing, please email me so I can make the translation flow better.}, archivePrefix = {arXiv}, author = {Euler, Leonhard}, citeulike-article-id = {3036294}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0504172}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0504172}, eprint = {math/0504172}, keywords = {available-in-tex-format, historical-work, mathematics, number-theory}, month = {Apr}, posted-at = {2008-07-23 08:53:19}, priority = {2}, title = {An algebraic problem of finding four numbers, given the products of each of the numbers with the sum of the three others}, url = {http://arxiv.org/abs/math/0504172}, year = {2005} }

TY - ELEC ID - citeulike:3036294 L3 - citeulike-article-id:3036294 N2 - In this paper Euler considers the problem of given a,b,c,d where a=v(x+y+z), b=x(v+y+z), c=y(v+x+z), d=z(v+x+y), determining v,x,y,z. He makes many changes of variable and ends up with four nicer equations, each in terms of a new variable u and the constants a,b,c,d. I do not understand exactly what Euler is doing, but I think the translation is ``correct''. If anyone understands what Euler is doing, please email me so I can make the translation flow better. TI - An algebraic problem of finding four numbers, given the products of each of the numbers with the sum of the three others KW - available-in-tex-format KW - historical-work KW - mathematics KW - number-theory AU - Euler, Leonhard PY - 2005/Apr/08/ UR - http://arxiv.org/abs/math/0504172 ER -