query: Number of solutions for $x^2 \equiv x \pmod m$
positive_passages.docid: 7303
positive_passages.text: How many idempotent elements does the ring ${\bf Z}_n$ contain?
negative_passages.docid: 119109
negative_passages.text: Integer solutions to $ n^2 + 1 = 2 \times 5^m$
negative_passages.docid: 4129
negative_passages.text: Solvability of $a \equiv x^2 \mod b$
negative_passages.docid: 15314
negative_passages.text: Number of solutions to $x^n \equiv 1 \mod p$
negative_passages.docid: 94407
negative_passages.text: Number of solutions for $x[1] + x[2] + \ldots + x[n] =k$
negative_passages.docid: 135465
negative_passages.text: Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
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: 103197
negative_passages.text: number of distinct solution of Integral equation
negative_passages.docid: 26478
negative_passages.text: Show that the congruence $x^{p-1} \equiv 1 \pmod {p^2}$ has precisely $p-1$ solutions modulo $p^2$
negative_passages.docid: 66161
negative_passages.text: How to solve the equation $n^2 \equiv 0 \pmod{584}$?
negative_passages.docid: 80843
negative_passages.text: Find all solutions to $x^9 \equiv 25 \pmod {29}$
negative_passages.docid: 128107
negative_passages.text: find all $ a \in \mathbb N $ such that $2^a − 1 \equiv 0 \pmod 3$ and $ 4x^2 + 1 \equiv 0 \pmod {\frac{2^a -1}{3}}$ has a solution
negative_passages.docid: 22962
negative_passages.text: How to show $\binom{2p}{p} \equiv 2\pmod p$?
negative_passages.docid: 72023
negative_passages.text: Integer solutions of the equation $x^2+y^2+z^2 = 2xyz$
negative_passages.docid: 115244
negative_passages.text: Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
negative_passages.docid: 59442
negative_passages.text: Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
negative_passages.docid: 93820
negative_passages.text: Fermat's little theorem applied for $n$'th root existence $\!\bmod p$