Oblivious transfer algorithm's page on Wikipedia claims:
The receiver picks a random $x$ modulo $N$ and sends $x^2 \bmod N$ to the sender Note that $\gcd(x,N)=1$ with overwhelming probability, which ensures that there are $4$ square roots of $x^2 \bmod N$.
The main idea here is that given $N$ and $x^2 \bmod N$, there are $4$ and only $4$ possible $x$ values that can be deduced.
Why is that? Or what did I get wrong?
$N$ here is the product of two primes. Modulo a prime there are at most two square roots of any number, because $x^2 - a^2 = (x-a)(x+a)$. Use the Chinese Remainder Theorem.