query: Find all incongruent solutions to $x^2 \equiv 23 \pmod{77}$
positive_passages.docid: 50047
positive_passages.text: How do I use the Chinese remainder theorem to find all the square roots of 11 in $\mathbb Z_{35}$?
negative_passages.docid: 15314
negative_passages.text: Number of solutions to $x^n \equiv 1 \mod p$
negative_passages.docid: 94700
negative_passages.text: Integer solutions for $x^3+2=y^2$?
negative_passages.docid: 40063
negative_passages.text: $x^2+y^2=z^n$: Find solutions without Pythagoras!
negative_passages.docid: 41673
negative_passages.text: Solve congruence system $\ x\equiv m_i-1 \pmod{m_i}\,$ for $\,i = 1,\ldots, k$
negative_passages.docid: 34192
negative_passages.text: Solve $x^{5} \equiv 2$ mod $221\ $ [Taking modular $k$'th roots if unique]
negative_passages.docid: 21679
negative_passages.text: Solving $x^3-y^3=xy+61$ in integers
negative_passages.docid: 61877
negative_passages.text: Find all integer solutions to Diophantine equation $x^3+y^3+z^3=w^3$
negative_passages.docid: 133925
negative_passages.text: Find All Solutions to System of Congruence
negative_passages.docid: 69874
negative_passages.text: Are there any integer solutions to $a^3=b^2$?
negative_passages.docid: 152591
negative_passages.text: For which prime numbers $p$ does the congruence $x^2 + x + 1 \equiv 0 \pmod{p}$ have solutions?
negative_passages.docid: 81058
negative_passages.text: Evaluate $6^{433} \pmod {21}$ and a proving question
negative_passages.docid: 131941
negative_passages.text: Solve quadratic congruences.
negative_passages.docid: 110809
negative_passages.text: What can primes, except 2, 3, and 5, be congruent to $\pmod {30}$?
negative_passages.docid: 143754
negative_passages.text: Finding the solution of the congruence $4x\equiv16\pmod{26}$
negative_passages.docid: 144863
negative_passages.text: Finding integer solutions to $y^2=x^3-2$
negative_passages.docid: 75489
negative_passages.text: Solve $x^2$ $mod$ $23 = 7^2$