Zimian问题实质上是叙拉古算子方程 xi = S xi(xi >1)的解的存在性问题,Erd?s给出长度 m i =1 i = 1= 8的一组解.本文不仅给出了叙拉古算子方程有解的一个必要条件,指出了方程不存在长度 m = 1的解,还给出了方程在长度 m = 18, m...Zimian问题实质上是叙拉古算子方程 xi = S xi(xi >1)的解的存在性问题,Erd?s给出长度 m i =1 i = 1= 8的一组解.本文不仅给出了叙拉古算子方程有解的一个必要条件,指出了方程不存在长度 m = 1的解,还给出了方程在长度 m = 18, m = 13, = 10, = 8 和 m = 5 的若干组解.展开更多
The oldest Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. The recent proof [1] connected Goldbach’s Conjecture with the fact...The oldest Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. The recent proof [1] connected Goldbach’s Conjecture with the fact that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes. The present paper contains explicit additional and complementary details of the proof, insisting on the existence and the number of Goldbach’s representations of even positive integers as sums of pairs of primes.展开更多
Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. This paper contains the proof that every positive composite integer n strictly...Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. This paper contains the proof that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes, which implicitly proves Goldbach’s Conjecture for 2n as well.展开更多
文摘Zimian问题实质上是叙拉古算子方程 xi = S xi(xi >1)的解的存在性问题,Erd?s给出长度 m i =1 i = 1= 8的一组解.本文不仅给出了叙拉古算子方程有解的一个必要条件,指出了方程不存在长度 m = 1的解,还给出了方程在长度 m = 18, m = 13, = 10, = 8 和 m = 5 的若干组解.
文摘The oldest Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. The recent proof [1] connected Goldbach’s Conjecture with the fact that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes. The present paper contains explicit additional and complementary details of the proof, insisting on the existence and the number of Goldbach’s representations of even positive integers as sums of pairs of primes.
文摘Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. This paper contains the proof that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes, which implicitly proves Goldbach’s Conjecture for 2n as well.
