Euler's Sum Of Powers Conjecture
Euler's conjecture is a disproved conjecture in mathematics related to Fermat's last theorem which was proposed by Leonhard Euler in 1769. It states that for all integers n and k greater than 1, if the sum of n kth powers of positive integers is itself a kth power, then n is greater than or equal to k.
In symbols, if 
where and are positive integers, then .
The conjecture represents an attempt to generalization of Fermat's last theorem, which could be seen as the special case of n = 2: if, then .
Although the conjecture holds for the case of k = 3 (which follows from Fermat's last theorem for the third powers), it was disproved for k = 4 and k = 5. It still remains unknown if the conjecture fails or holds for any value k ≥ 6.
Read more about Euler's Sum Of Powers Conjecture: Generalizations
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