This lemma was presented by Hua Luogeng in his paper "On Waring's Problem". His objective was to give a proof that Hardy and Littlewood's asymptotic formula for the Diophantine equation is also true for k less than 14.
Hua Luogeng was a renowned mathematician famous for his contributions to number theory. He had formal education of six years in primary school and three years in middle school, and never got a formal degree from any university. His seminal work on Waring's problem established his reputation while he studied the Hardy-Littlewood circle method in number theory.
Andrew Wiles proved a generalized version of what Pierre de Fermat stated in the margin of a copy of the works of Diophantus. He showed his proof on 6/23, 1993 at the Newton Institute in Cambridge, England.