Find all the incongruent solutions of the following quadratic congruence.

X^2 is congruent to 53 mod 143

2. Originally Posted by JCIR
X^2 is congruent to 53 mod 143
This is equivalent to,
$x^2\equiv 54 (\bmod 11)$ and $x^2\equiv 54(\bmod 13)$
Which reduces to,
$x^2 \equiv 10 (\bmod 11)$ and $x^2 \equiv 2(\bmod 13)$
This has no solutions.

3. Originally Posted by ThePerfectHacker
This is equivalent to,
$x^2\equiv 54 (\bmod 11)$ and $x^2\equiv 54(\bmod 13)$
Which reduces to,
$x^2 \equiv 10 (\bmod 11)$ and $x^2 \equiv 2(\bmod 13)$
This has no solutions.
The question asked for 53, not 54.

And this question is the same as occurred in this thread.