From a recent question on putative names for the sum of the real part and the imaginary part of a complex number at SE.DSP (Technical Term for the Sum I + Q), I was wondering whether there are names for the complex quantity $1+i$, which is the smallest of the Gaussian primes. I have checked in my versions of the books:

Since it also plays a role in definitions for Gaussian Mersenne numbers ($(1 \pm i)^n-1$ or $-i((1+i)^n-1)$), I hoped it was given a specific name in the literature, and I could not find any so far.

  • 3
    $\begingroup$ The Gaussian integer $1+i$ is analogous to the integer $2$: every Gaussian integer $a+bi$ is either "even" (meaning that $a+bi \equiv 0 \pmod {1+i}$, which is equivalent to $a$ and $b$ having the same parity) or "odd" (meaning that $a+bi \equiv 1 \pmod {1+i}$, which is equivalent to $a$ and $b$ having opposite parities), but not both. $\endgroup$ Jun 14, 2020 at 17:44


You must log in to answer this question.