Stumped by a notation. I'm reading through < and came across the following notation on p. 1: > For example, a squarefree positive integer $p \in 1 + 4\Bbb Z$ is prime if and only if the equation $4x^2 + y^2 = p$ has an odd number of positive solutions $(x,y)$. What I'm confused about is the use of the blackboard bold expression $1+4\Bbb Z$ as a restriction on the $p$ variable. I've seen field theorists use stuff like $p \in {\Bbb Z}/12{\Bbb Z}$ for a finite field element, but this one is new to me.

The set $1+4\mathbb{Z}$ is the set of integers $x$ such that $x$ is congruent to $1$ modulo $4$. More familiarly, $4\mathbb{Z}$ is the ideal of all multiples of $4$.

The notation $1+4\mathbb{Z}$ is not all that far away from the old-fashioned "of the form $4k+1$."