# Math Help - Quadratic Congruences...

Hello,
I would really appreciate it if someone could please show me how to solve :

Find x when 3(x^2) + 1 ≡ 0 (mod 7).
step by step.
It's from a sample exam I am trying to study..

2. Originally Posted by alireza6485
Hello,
I would really appreciate it if someone could please show me how to solve :

Find x when 3(x^2) + 1 ≡ 0 (mod 7).
step by step.
It's from a sample exam I am trying to study..

The following is done via arithmetic modulo 7:

$3x^2+1=0\Longrightarrow 3x^2=-1=6\Longrightarrow x^2=2\Longrightarrow x=\pm 3\Longrightarrow x_1=3\,,\,x_2=-3=4$

Tonio

3. Thank you for your help...
do you know any good website with tutorials about quadratic congruences and RSA?