Commit 78b21d53 authored by Freek Wiedijk's avatar Freek Wiedijk
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Merge branch 'master' of

parents 34254bcc 63d0abb8
......@@ -402,7 +402,7 @@ We define the basic operations ($+, -, \times$) with their respective neutral
elements ($0, 1$) and prove \lref{lemma:Zmodp_field}.
$\F{p}$ is a commutative field.
$\F{p}$ is a field.
For $a = 486662$, by using the Legendre symbol we prove that
$a^2 - 4$ and $2$ are not squares in $\F{p}$.
......@@ -452,8 +452,8 @@ For all $x \in \F{p}$, we can compute $x^3 + ax^2 + x$. Using \lref{lemma:square
we can find a $y$ such that $(x,y)$ is either on the curve or on the quadratic twist:
For all $x \in \F{p}$, there exists a point $P$ over $M_{486662,1}(\F{p})$ or
over $M_{486662,2}(\F{p})$ such that the \xcoord of $P$ is $x$.
For all $x \in \F{p}$, there exists a point $P$ in $M_{486662,1}(\F{p})$ or
in $M_{486662,2}(\F{p})$ such that the \xcoord of $P$ is $x$.
Theorem x_is_on_curve_or_twist:
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