# Tagged Questions

48 views

### Finding the number of elements in $\left(ℤ[i]\right)_m$

If $m$ = $m_1$ + $m_1i$ ∈ $ℤ[i]$, is there a general formula to find the number of elements in $\left(ℤ[i]\right)_m$?
39 views

### Number theory proof regarding norms

How would you prove that if $x$ is a prime in $ℤ[i] \Longleftrightarrow$ $N(x)$ is a prime in $ℤ$ N(x) represents the norm of x.
178 views

158 views

### Why don't we define division by zero as an arbritrary constant such as $j$? [duplicate]

Why don't we define $\frac 10$ as $j$ , $\frac 20$ as $2j$ , and so on? I know that by following the rules of math this eventually leads to $1=2$ , but we could make an exception and say that $j$ is ...
90 views

### Solving complex linear congruences

Find $x \in \mathbb{Z}[i]$ such that: $(1+2i)x \equiv 1 \mod 3+3i$ How would you go about doing this? Best I can think of is keep guessing....
### Lerch-$\small \zeta(\varphi,0,-n)$ of integer *n* purely real and imaginary ($\small \zeta_\varphi (-n)^2$ is real) for $\small n \ge 2$?
Are the Lerch-$\zeta(\varphi,0,-n)$ of integer n (for shortness I use the notation of my earlier question $\small \zeta_\varphi(-n)$) periodically purely real and imaginary: $\zeta_\varphi (-n)^2$ ...