2 citations · 3 across the 7 of their papers we have counts for
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An equation about sum of primes with digital sum constraints
Haifeng Xu
We know that any prime number of form can be written as a sum of two perfect square numbers. As a consequence of Goldbach's weak conjecture, any number great than can b…
The largest cycles consist by the quadratic residues and Fermat primes
Haifeng Xu
This paper studies the largest cycles consisted by the quadratic residues modulo prime numbers. We give some formulae about the maximum length of the cycles. Especially, the formul…
An alternative proof of the Dirichlet prime number theorem
Haifeng Xu
Dirichlet's theorem on arithmetic progressions called as Dirichlet prime number theorem is a classical result in number theory. Atle Selberg\cite{Selberg} gave an elementary proof…
Periodicity related to a sieve method of producing primes
Haifeng Xu, Zuyi Zhang, Jiuru Zhou
In this paper we consider a slightly different sieve method from Eratosthenes' to get primes. We find the periodicity and mirror symmetry of the pattern.
The connection between the Basel problem and a special integral
Haifeng Xu, Jiuru Zhou
By using Fubini theorem or Tonelli theorem, we find that the zeta function value at 2 is equal to a special integral. Furthermore, We find that this special integral is two times o…