query: Compute $\sqrt{x} \pmod p$ working on finite fields.
positive_passages.docid: 141704
positive_passages.text: Fractional exponentiation in modular arithmetic
negative_passages.docid: 148458
negative_passages.text: $x^p-x \equiv x(x-1)(x-2)\cdots (x-(p-1))\,\pmod{\!p}$
negative_passages.docid: 113481
negative_passages.text: Modular Arithmetic - Find the Square Root
negative_passages.docid: 22029
negative_passages.text: Solving modular arithmetic questions
negative_passages.docid: 57884
negative_passages.text: Number of monic irreducible polynomials of prime degree $p$ over finite fields
negative_passages.docid: 86174
negative_passages.text: Finding an isomorphism between these two finite fields
negative_passages.docid: 151636
negative_passages.text: Fast way to calculate n! mod m where m is prime?
negative_passages.docid: 23153
negative_passages.text: $\bmod p\!:\ x^2\equiv 1\iff x\equiv \pm1\ $ for prime $p$
negative_passages.docid: 117789
negative_passages.text: Computing Galois Group of $\mathbb{Q}(\sqrt{2},\sqrt{3}):\mathbb{Q}$
negative_passages.docid: 3703
negative_passages.text: Order of finite fields is $p^n$
negative_passages.docid: 104176
negative_passages.text: $15x\equiv 20 \pmod{88}$ Euclid's algorithm
negative_passages.docid: 134450
negative_passages.text: Chinese Remainder Theorem $\ x\equiv m_k-2\pmod{m_k}$
negative_passages.docid: 130342
negative_passages.text: Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
negative_passages.docid: 95692
negative_passages.text: Factoring polynomials of the form $1+x+\cdots +x^{p-1}$ in finite field
negative_passages.docid: 44033
negative_passages.text: Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$
negative_passages.docid: 23712
negative_passages.text: $F$ is a finite field of size $s$. Prove that if $s=2^m$ for some $m>0$, then all elements of F have a square root.
negative_passages.docid: 51153
negative_passages.text: Number of solutions to $x^2\equiv a\pmod m$