query: Solve $x^2 + x + 47 ≡ 0 \pmod {7^3}$
positive_passages.docid: 155659
positive_passages.text: Is there a formula for solving the congruence equation $ax^2 + bx + c=0$?
negative_passages.docid: 67015
negative_passages.text: Solve $x^2 + 8 = 3^n$, where $x\in\mathbb N$.
negative_passages.docid: 143878
negative_passages.text: Solve: $\int x^3\sqrt{4-x^2}dx$
negative_passages.docid: 112390
negative_passages.text: Solutions of $x^2 \equiv 1 \pmod N$
negative_passages.docid: 15436
negative_passages.text: Find p and q s.t. $({p-1})^{q-1}+({q-1})^{p-1} \equiv 101 \pmod {pq}$
negative_passages.docid: 131395
negative_passages.text: Solving linear congruence $2x + 11 \equiv 7 \pmod 3$
negative_passages.docid: 133164
negative_passages.text: Rational solutions for $x^2+y^2=3$
negative_passages.docid: 70692
negative_passages.text: Solve $x^2+2=y^3$ using infinite descent?
negative_passages.docid: 142769
negative_passages.text: Let $f(x) =7x^{32}+5x^{22}+3x^{12}+x^2$. Then find its remainder in the following cases.
negative_passages.docid: 46400
negative_passages.text: how do i prove that $17^n-12^n-24^n+19^n \equiv 0 \pmod{35}$
negative_passages.docid: 51153
negative_passages.text: Number of solutions to $x^2\equiv a\pmod m$
negative_passages.docid: 26692
negative_passages.text: Equation in integers $7^x-3^y=4$
negative_passages.docid: 138078
negative_passages.text: Solve $2000x^6+100x^5+10x^3+x-2=0$
negative_passages.docid: 107008
negative_passages.text: Find the remainder when $45!$ is divided by $47$?
negative_passages.docid: 77024
negative_passages.text: Find the number of solutions of $x^2=x\mod m$ for any integer $m$
negative_passages.docid: 103274
negative_passages.text: Integer solutions to the equation $a^3+b^3+c^3=30$
negative_passages.docid: 106308
negative_passages.text: how do you solve $x^x=x$