tag:blogger.com,1999:blog-12535639.post116425414444018144..comments2017-10-13T09:32:13.753-07:00Comments on Fermat's Last Theorem: Nicolo Fontana TartagliaLarry Freemanhttp://www.blogger.com/profile/06906614246430481533noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-12535639.post-86841462494323461712013-05-06T16:06:26.553-07:002013-05-06T16:06:26.553-07:00Can one use Cardano's solution to the cubic to...Can one use Cardano's solution to the cubic to show the impossibility of integer solutions to <br />9r^3 - t^3 - s^3 = 6rst<br /><br />I know this can be done by converting the equation to a more complex equation of an elliptical curve using computer analysis, but I'm wondering if there is an easier way.<br /><br />Obviously, if you replace 9r^3 with 8r^3, there are infinite integer solutions with 2r = t+sUnknownhttps://www.blogger.com/profile/08173782986738085246noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-54621425041785832502013-05-06T16:04:11.486-07:002013-05-06T16:04:11.486-07:00Can one use Cardano's solution to the cubic to...Can one use Cardano's solution to the cubic to prove the impossibility of integer solutions to <br />9r^3 - s^3 - t^3 = 6rst<br /><br />I know this can be shown impossible with a computer analysis after this is converted into a more complex equation of an elliptical curve, but I'm wondering if there is an easier method using Cardano's solution to the cubic.Unknownhttps://www.blogger.com/profile/08173782986738085246noreply@blogger.com