Euler's sum of powers conjecture: Difference between revisions
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There is a conjecture in mathematics that held for over two hundred years before it was disproved by the finding of a counterexample in 1966 by [http://www.ams.org/journals/mcom/1967-21-097/S0025-5718-1967-0220669-3/S0025-5718-1967-0220669-3.pdf Lander and Parkin].
This conjecture is called [[wp:Euler's sum of powers conjecture|Euler's sum of powers conjecture]] and can be stated as such:
:<big>At least k positive k<sup>th</sup> powers are required to sum to a k<sup>th</sup> power, except for the trivial case of one
▲ except for the trivial case of one k<sup>th</sup> power: y<sup>k</sup> = y<sup>k</sup> </big>
In 1966,
The task consists in writing a program to search for an integer solution of <math>x_0^5 + x_1^5 + x_2^5 + x_3^5 = y^5</math> where all <math>x_i</math> and <math>y</math> are distinct integers between 0 and 250 (exclusive). Show an answer here.
▲In 1966, Leon J. Lander and Thomas R. Parkin used a brute-force search on a [[wp:CDC_6600|CDC 6600]] computer restricting numbers to those less than 250.
▲;Related tasks:
▲* [[Pythagorean quadruples]].
▲* [[Pythagorean triples]].
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