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Euler's sum of powers conjecture
Euler's sum of powers conjecture, also called the Euler quartic conjecture, is a disproved 1769 conjecture of Leonhard Euler that at least n nth powers are needed to sum to an nth power.
Waring–Goldbach problem
The Waring–Goldbach problem is a question in additive number theory asking how few kth powers of primes suffice to represent large integers, merging Waring's problem with Goldbach's.
Waring's problem
Waring's problem, posed by Edward Waring in 1770, asks how many k-th powers suffice to represent every natural number as a sum; Hilbert proved a bound exists in 1909.