(But not consecutive) On Sat, May 9, 2020 at 3:35 PM Mike Stay <metaweta@gmail.com> wrote:
There are infinitely many solutions to a^4 + b^4 + c^4 + d^4 = (a + b + c + d)^4 https://en.wikipedia.org/wiki/Jacobi%E2%80%93Madden_equation
On Fri, May 8, 2020 at 1:18 PM Dan Asimov <dasimov@earthlink.net> wrote:
Famously,
1^2 + 2^2 + 3^2 + ... + 24^2 = 70^2
is the only case where the sum of an initial sequence of squares equals another square (ignoring 1^2 = 1^2).
Are there any non-trivial examples of this for powers higher than 2 ?
(For non-initial cases, 3^3 + 4^3 + 5^3 = 6^3 is the first example, and this website <https://www.mathpages.com/home/kmath147.htm> gives many other examples for cubes.)
But I'm interested in when 1^k + 2^k + ... + n^k is an exact kth power for k > 2 and of course n > 1.
—Dan
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-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com