对复整数集Z[i]中高斯定理的注记

Annotations on Gowers Theory in Complex Integer Set Z[i]

本文主要是对Z[i]中的高斯定理做了进一步的讨论,给出了满足p=a_1~2+a_2~2中的a_1,a_2的求法,并指出了其中的a_1~2,a_2~2是被p唯一决定的一对数,同时还给出了适合p^2=a^2+b^2中的a,b的求法,其中,p为奇素数,且适合p≡1(mod 4)。

The paper mainly goes further into Gowers theory in Z[i] provides thesolving method of a_1 and a_2 which satisfy p = a_1~2 + a_2~2 and indicates that a_l and a_2 area pair of number which P is only decided by P. In the meantime, it also providesthe solving method of a and b which fit p^2 = a^2 + b^2, among which is odd prime andit fits p≡1(mod4).