A slightly clumsy omission from the Wikipedia pages is that these power-sums are equal also for 0-th powers: so `ideal' solutions satisfy just as many equations as there are members of each set. The `odious/evil' solution with Thue-Morse sequence connection seems astonishing, and remains at present inexplicable to me! WFL On 6/28/17, Dan Asimov <asimov@msri.org> wrote:
Fascinating! Thanks.
—Dan
On Jun 28, 2017, at 1:50 PM, Hans Havermann <gladhobo@bell.net> wrote:
I wrote:
I recently saw in a book an example of two disjoint sets of integers whose sums of nth powers are equal for n = 1, 2, 3, 4, 5.
https://en.wikipedia.org/wiki/Prouhet–Tarry–Escott_problem
Click on the French version of the wiki for more examples.
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