本文讨论了n个正整数的和与积相等的一个必要条件,并证明了两个与素数、合数有关的结论。结论1:若n(n≥2)个正整数a_1,a_2,…,a_n满足条件sum from i=1 to n a_i=multiply from i=1 to n a_i,则a_i≤n(i=1,2,…,n)。证明:(1)当n=2时,a_1·a_2-(a_1+a_2)=(a_1-1)·(a_2-1)-1≥0,当且仅当a_1=a_2=2时等号成立,故a_1·a_2=(a_1+a_2)时a_1≤2,a_2≤2,符合结论1。 In this paper, we discuss a necessary condition that the sum of n positive integers is equal to the product, and prove two conclusions about the prime numbers and the composite numbers. Conclusions 1: If n (n≥2) positive integers a_1, a_2, ..., a_n satisfy the condition sum from i = 1 to n a_i = multiply from i = 1 to n a_i, then a_i≤n (i = 1,2 , ..., n). Proof: (1) When n = 2, a_1 · a_2- (a_1 + a_2) = (a_1-1) · (a_2-1) -1≥0 if and only if a_1 = a_2 = 2 Therefore, when a_1 · a_2 = (a_1 + a_2), a_1≤2 and a_2≤2, which are consistent with conclusion 1.