[math-fun] Taxicab 5.2.2 / A046881
As a programming exercise I just finished a search for a solution A⁵ + B⁵ = C⁵ + D⁵ for numbers up to 4.25e37 ( 2 ^ 125 ) but did not find anything. This is perhaps not a surprise, since the density of possible solutions falls precipitously. I ran the search over a couple of days on 8 x Tesla V100 GPUs, and can give details if anyone is interested. But my main point of curiosity now is what the current thinking about this open problem is: Do any taxicab numbers exist for powers >= 5 ? Is it even something that is tackled seriously ? Frank
You could Compare: https://link.springer.com/article/10.1007/s40993-016-0058-2 https://www.ams.org/journals/bull/2007-44-04/S0273-0979-07-01178-0/S0273-097... The "Dwork Family" is similar, well studied, and more flexible. Are integer solutions well known there or no? --Brad On Fri, Oct 9, 2020 at 12:06 PM Frank Stevenson < frankstevensonmobile@gmail.com> wrote:
As a programming exercise I just finished a search for a solution A⁵ + B⁵ = C⁵ + D⁵ for numbers up to 4.25e37 ( 2 ^ 125 ) but did not find anything. This is perhaps not a surprise, since the density of possible solutions falls precipitously. I ran the search over a couple of days on 8 x Tesla V100 GPUs, and can give details if anyone is interested.
But my main point of curiosity now is what the current thinking about this open problem is: Do any taxicab numbers exist for powers >= 5 ? Is it even something that is tackled seriously ?
Frank _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Swinnerton-Dyer had a paper, I think from the 1950s, that has a parametric solution to A5+B5+C5=D5+E5+F5. ---Rich ---- Quoting Frank Stevenson <frankstevensonmobile@gmail.com>:
As a programming exercise I just finished a search for a solution A? + B? = C? + D? for numbers up to 4.25e37 ( 2 ^ 125 ) but did not find anything. This is perhaps not a surprise, since the density of possible solutions falls precipitously. I ran the search over a couple of days on 8 x Tesla V100 GPUs, and can give details if anyone is interested.
But my main point of curiosity now is what the current thinking about this open problem is: Do any taxicab numbers exist for powers >= 5 ? Is it even something that is tackled seriously ?
Frank _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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