Hi Roger, nice to hear from you. Are you still in Santa Fe nowadays? If so, why not drop by Friam at St John's and chat about this? Sounds fascinating!
It's interesting that so few numbers we stumble across are really large. And how limited numbers are in computing like in JavaScript, which does have a BigInt but it isn't good for really huge numbers. There is a good library for huge: https://github.com/mikemcl/bignumber.js/. It would be nice if the GPU could handle them. -- Owen On Sat, May 9, 2026 at 8:24 PM Roger Frye <[email protected]> wrote: > Friends, > > I just found 2 more today on my birthday. People ask me why I keep > searching for more integer solutions to A^4 + B^4 + C^4 = D^4 . > > Some mathematicians are satisfied to have a proof that there are an > infinite number of solutions, not finite, or zero. > > Statisticians worry about gaps in the distribution known of > solutions.There is a suspicious dearth around 10^10 . > > As a computer jock, I am interested in the algorithms and the bridges > between different mathematical formulations. I found a new way to do brute > force searching. I’ve refined the two known elliptic curve methods and > found a way to use the duality between them. I am searching for isogenies > between the elliptic and hyperelliptic curves, but that problem is > cryptographically hard. Yet I see patterns that keep me trying. > > Assistance from AI is laughable at this level of invention. Coding > assistants just suggest ways to patch over bugs rather than uncover root > causes. Deeper level suggestions for strategy lead down blind alleys almost > all the time. I am sure AI will get better, but for now my experience and > persistence are winning. > > -Roger -- still looking for a job. > .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / > ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. > FRIAM Applied Complexity Group listserv > Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom > https://bit.ly/virtualfriam > to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: 5/2017 thru present > https://redfish.com/pipermail/friam_redfish.com/ > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ >
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