9 Oct
2020
9 Oct
'20
11:05 a.m.
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