On Erd(?)s-Graham-Spencer Conjecture

In this thesis,we mainly research on Erd(?)s-Graham-Spencer Conjecture.The main results are summarized as follows.In 1980,Erd(?)s,Graham and Spencer posed the conjecture:if a1≤a2 ≤…as are integers with(?),then this sum can be decomposed into n parts so that all partial sum are ≤ 1.This is not true for(?)as shown bya1=a2=…an-2=1,an-1=2,an=an+1＝3,an+2=…an+5 = 5.In 2008,Jin-Hui Fang and Yong-Gao Chen proved the result:if a1≤a2≤…≤as are integers with(?),then this sum can be decomposed into n parts so that all partial sum are ≤ 1.In this thesis,we extend the above result and obtain the following result(Colloq.Math.151(2018),203-215.):If a1≤a2≤…≤as are integers with(?),then this sum can be decomposed into n parts so that all partial sum are≤1.