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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