# Thread: Find all solutions of...

1. ## Find all solutions of...

i) Find (just by trial and error) all solutions of

2x2 is congruent to 1 mod 17
and
2x2 is congruent to 1 mod 23
ii) Now find all solutions of
2x2 is congruent to 1 mod 391
[Note: 391 = 17*23]

2. Did you mean to write?

$\displaystyle 2x^2 \equiv 1 \pmod{17}$ and $\displaystyle 2x^2 \equiv 1\pmod{23}$

3. Note that if :

$\displaystyle x \equiv y \pmod{m}$

$\displaystyle x \equiv y \pmod{n}$

Then :

$\displaystyle x \equiv y \pmod{mn}$

$\displaystyle 2x^2 \equiv 1 \pmod{17}$ and $\displaystyle 2x^2 \equiv 1\pmod{23}$