8
votes
1answer
111 views

Wikipedia claims that number theorists tend to prefer $0 \notin \mathbb{N}$. Is this actually true?

According to wikipedia here: $\mathbb{N}$ means either $\{ 0, 1, 2, 3, ...\}$ or $\{ 1, 2, 3, ...\}.$ The choice depends on the area of mathematics being studied; e.g. number theorists ...
2
votes
1answer
222 views

How many solutions for $x^2 = 1$?

Let $F$ be an non-archimedean local field, let $o$ be its ring of integers, and let $p$ be the maximal ideal Is there a closed form for the cardinality $$ | \{ x \in o / p^N: x^2 = -1 \bmod p^N\} | ...