query: Quadratic Modular Arithmetic
positive_passages.docid: 21108
positive_passages.text: Perfect squares and modularly congruency in mod 5
negative_passages.docid: 45882
negative_passages.text: Solving a congruence without Fermat's little theorem
negative_passages.docid: 134450
negative_passages.text: Chinese Remainder Theorem $\ x\equiv m_k-2\pmod{m_k}$
negative_passages.docid: 68252
negative_passages.text: Chinese Remainder Theorem solvability for non-coprime moduli
negative_passages.docid: 80754
negative_passages.text: A slight modification in Chinese Remainder Theorem
negative_passages.docid: 45014
negative_passages.text: Modular exponentiation by repeated squaring
negative_passages.docid: 153111
negative_passages.text: factoring a quadratic equation
negative_passages.docid: 25910
negative_passages.text: Product of Quadratic Residues
negative_passages.docid: 21874
negative_passages.text: Solve $x^3+x \equiv 1 \pmod p$
negative_passages.docid: 81669
negative_passages.text: The logic of the AC Method of factoring quadratic polynomials
negative_passages.docid: 4972
negative_passages.text: Mod of numbers with large exponents [modular order reduction]
negative_passages.docid: 67899
negative_passages.text: Integer squares of the form $x^4+x^3+x^2+x+1$
negative_passages.docid: 58368
negative_passages.text: Proof of Unique Solution for Modular Exponentiation In Cryptography
negative_passages.docid: 17786
negative_passages.text: Existence of Consecutive Quadratic residues
negative_passages.docid: 9039
negative_passages.text: What is the best way to solve modular arithmetic equations such as $9x \equiv 33 \pmod{43}$?
negative_passages.docid: 29231
negative_passages.text: Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
negative_passages.docid: 60305
negative_passages.text: Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$