[FRIAM] My New Results on Euler's Conjecture

[Pieter Steenekamp]

Impressive work Roger!

On another note: I emailed you directly regarding your request for
challenging programming work.


On Fri, Feb 6, 2026, 9:37 PM Roger Frye <frye.roger at gmail.com> wrote:

> In 1988, Noam Elkies at Harvard and I collaborated on finding
> counter-examples to Euler’s 1769 conjecture about sums of 4th powers. He
> proved that there are an infinite number of counter-examples, and I used
> all of the Connection Machines at Thinking Machines to find the smallest.
>
> Since then, other researchers have used variations of my brute force
> technique and Elkies’ Elliptic Curve technique to extend the number of
> known solutions. As of yesterday, there were 93 solutions less than 1e27.
> Today I found 4 more with a newer Elliptic Curve technique.
>
> I published my result as a comment at Math StackExchange:
> https://math.stackexchange.com/questions/4857229/on-why-solutions-to-x4y4z4-1-come-in-pairs/5123321
>  .
>
> The code I used is in my GitHub repository: https://github.com/rfryeSigma
>  .
>
> -Roger
> p.s. I am looking for programming work. I specialize in Machine Learning
> and physics simulations, but I would be interested in anything challenging.
> .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. /
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