query: If t is a quadratic residue mod p, how can I efficiently solve the equation $x^2=t \pmod {p}$?
positive_passages.docid: 144017
positive_passages.text: How to find the smallest $n$ such that $n^a\equiv 1 \pmod p$
negative_passages.docid: 71482
negative_passages.text: Solve $p_4(x) = x^4 −(2m + 4)x^2 + (m−2)^2 $such that $p_4$ is a product of two non-constant integer-coeficient polynomials
negative_passages.docid: 7085
negative_passages.text: Prove that if the equation $x^{2} \equiv a\pmod{pq}$ has any solutions, then it has four solutions.
negative_passages.docid: 140198
negative_passages.text: Let $a$ be a quadratic residue modulo $p$. Prove that the number $b\equiv a^\frac{p+1}{4} \mod p$ has the property that $b^2\equiv a \mod p$.
negative_passages.docid: 36941
negative_passages.text: If $p$ is congruent to $2 \pmod 3$, how can I prove that all $a$, $1 \le a \le p-1$ are cubic residues $\mod p$?
negative_passages.docid: 13904
negative_passages.text: $p = x^2 + xy + y^2$ if and only if $p \equiv 1 \text{ mod }3$?
negative_passages.docid: 123441
negative_passages.text: Quadratic congruences problem $(x^2-a)(x^2-b)(x^2-ab)$ ≡ 0 (mod p)
negative_passages.docid: 21874
negative_passages.text: Solve $x^3+x \equiv 1 \pmod p$
negative_passages.docid: 6160
negative_passages.text: How to prove a number $a$ is quadratic residue modulo $n$?
negative_passages.docid: 22029
negative_passages.text: Solving modular arithmetic questions
negative_passages.docid: 8784
negative_passages.text: modulo version of the quadratic formula and Euler's criterion
negative_passages.docid: 15897
negative_passages.text: Solve a congruence $1978^{20}\equiv x\pmod{125}$
negative_passages.docid: 146053
negative_passages.text: Proving identities (mod $pq$) using Fermat's little theorem?
negative_passages.docid: 25910
negative_passages.text: Product of Quadratic Residues
negative_passages.docid: 67332
negative_passages.text: Sum of two squares modulo p
negative_passages.docid: 101349
negative_passages.text: $-1$ isn't a quadratic residue $\pmod{p}, p=4k+3$.
negative_passages.docid: 130300
negative_passages.text: Proof that every quadratic residue has two roots, modulo a prime