Editing Waring's problem (section)

==Relationship with Lagrange's four-square theorem==
Long before Waring posed his problem, [[Diophantus]] had asked whether every positive integer could be represented as the [[Lagrange's four-square theorem|sum of four perfect squares]] greater than or equal to zero. This question later became known as Bachet's conjecture, after the 1621 translation of Diophantus by [[Claude Gaspard Bachet de Méziriac]], and it was solved by [[Joseph-Louis Lagrange]] in his [[Lagrange's four-square theorem|four-square theorem]] in 1770, the same year Waring made his conjecture. Waring sought to generalize this problem by trying to represent all positive integers as the sum of cubes, integers to the fourth power, and so forth, to show that any positive integer may be represented as the sum of other integers raised to a specific exponent, and that there was always a maximum number of integers raised to a certain exponent required to represent all positive integers in this way.