The method for finding"heng-diameter"and"gui-length"in the Zhou Bi Suan Jing(Arithmetical Classic of the Zhou Gnomon)can be regarded as an application of linear interpolation, while that for finding sun s displacement in the Dayan Calendar is similar to the sum formula of arithmetical series proposed by Liu Hui.

In this paper,We given the generating functions,and brief expression;and the application to the descussion of arithmetic equal power series on a kind of new number related with stirling number.

They also remarked that Heath-Brown gave explicitly infinitely many 4-term arithmetic progressions,where each term can be written as sums of two squares.

It has been proved that the primes contain arbitrarily long arithmetic progressions.

In this article, we prove that the ternary Goladbach problem in arithmetic progression can be solved for almost all large positive moduli, where the moduli can be as large as AT1/6-ε.

Every large odd integer can be represeted as the sum of three primes which take from arithmetic progressions.