Connection between 171st and Waring Problems

Long before Waring posed his problem, Diophantus had asked whether every positive
                integer could be represented as the 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 M;ziriac, and it was solved
                by Joseph-Louis Lagrange in his 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.