query: Let $p,q$ be prime numbers , Find all the solutions to the congruence $x^2\equiv (p+q)x \pmod{pq}$
positive_passages.docid: 29989
positive_passages.text: Solve $x^2+5x+6 \equiv 0 \pmod{\!11\cdot 17}$
negative_passages.docid: 54286
negative_passages.text: Let $p$ a prime number, then prove that : $\sum \limits_{k=0}^{p} \binom {p}{k} \binom{p+k}{k} \equiv 2^p +1 \pmod{p^2}$
negative_passages.docid: 42032
negative_passages.text: Find all solutions to $x^2\equiv 1\pmod {91},\ 91 = 7\cdot 13$
negative_passages.docid: 144851
negative_passages.text: For a prime $p \equiv 1$ or $3$ (mod $8$), show that the equation $x^{2} + 2y^{2} = p$ has a solution.
negative_passages.docid: 131551
negative_passages.text: $pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes
negative_passages.docid: 103499
negative_passages.text: $x^2 \equiv a \mod p$, $\ x^2 \equiv b \mod p$, and $x^2 \equiv ab \mod p$, prove either all three are solvable or exactly one
negative_passages.docid: 158161
negative_passages.text: $\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})=\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ for $p_{1},p_{2}$ primes.
negative_passages.docid: 15314
negative_passages.text: Number of solutions to $x^n \equiv 1 \mod p$
negative_passages.docid: 45882
negative_passages.text: Solving a congruence without Fermat's little theorem
negative_passages.docid: 4129
negative_passages.text: Solvability of $a \equiv x^2 \mod b$
negative_passages.docid: 82016
negative_passages.text: Given $p^2+q^2+r^2+1=s+\sqrt{p+q+r-s}$, solve for $s$
negative_passages.docid: 21530
negative_passages.text: How many solutions of $\mod 63$ : $x^2=1 \pmod7 $ and $x^3=1\pmod 9$
negative_passages.docid: 85449
negative_passages.text: Show a,b,c congruences when $a^2+b^2=c^2$
negative_passages.docid: 66161
negative_passages.text: How to solve the equation $n^2 \equiv 0 \pmod{584}$?
negative_passages.docid: 131941
negative_passages.text: Solve quadratic congruences.
negative_passages.docid: 102204
negative_passages.text: Factoring product of two primes from solutions of congruence
negative_passages.docid: 36713
negative_passages.text: Solving multiple congruences by CRT = Chinese Remainder Theorem