If n is a positive integer,let f (n) denote the number of positive integer solutions (n 1,n 2,n 3) of the Diophantine equation 4/n=1/n_1 + 1/n_2 + 1/n_3.For the prime number p,f (p) can be split into f 1 (p) + f 2 (p)...If n is a positive integer,let f (n) denote the number of positive integer solutions (n 1,n 2,n 3) of the Diophantine equation 4/n=1/n_1 + 1/n_2 + 1/n_3.For the prime number p,f (p) can be split into f 1 (p) + f 2 (p),where f i (p) (i=1,2) counts those solutions with exactly i of denominators n 1,n 2,n 3 divisible by p.In this paper,we shall study the estimate for mean values ∑ p<x f i (p),i=1,2,where p denotes the prime number.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11071235)
文摘If n is a positive integer,let f (n) denote the number of positive integer solutions (n 1,n 2,n 3) of the Diophantine equation 4/n=1/n_1 + 1/n_2 + 1/n_3.For the prime number p,f (p) can be split into f 1 (p) + f 2 (p),where f i (p) (i=1,2) counts those solutions with exactly i of denominators n 1,n 2,n 3 divisible by p.In this paper,we shall study the estimate for mean values ∑ p<x f i (p),i=1,2,where p denotes the prime number.
