query: $x^2 \equiv 1 \pmod{p^\alpha}$ - number of solutions
positive_passages.docid: 19071
positive_passages.text: solution set for congruence $x^2 \equiv 1 \mod m$
negative_passages.docid: 102234
negative_passages.text: Show $a^p \equiv a \mod 2p$
negative_passages.docid: 148458
negative_passages.text: $x^p-x \equiv x(x-1)(x-2)\cdots (x-(p-1))\,\pmod{\!p}$
negative_passages.docid: 143754
negative_passages.text: Finding the solution of the congruence $4x\equiv16\pmod{26}$
negative_passages.docid: 29640
negative_passages.text: If $x \equiv 1 \pmod 3$ and $x \equiv 0 \pmod 2$, what is $x \pmod 6$?
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: 36043
negative_passages.text: If $ab \equiv r \pmod{p}$, and $x^2 \equiv a \pmod{p}$ then $y^2 \equiv b \pmod{p}$ for which condition of $r$?
negative_passages.docid: 20034
negative_passages.text: Does $a^2+b^2=1$ have infinitely many solutions for $a,b\in\mathbb{Q}$?
negative_passages.docid: 57639
negative_passages.text: Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$
negative_passages.docid: 34323
negative_passages.text: Prove that $a^{(p-1)/2} \equiv 1$ (mod p) and $a^{(p-1)/2} \equiv -1 \pmod p$
negative_passages.docid: 127945
negative_passages.text: Number of solutions to the congruence $x^q \equiv 1 \mod p$.
negative_passages.docid: 38379
negative_passages.text: Showing that $e^z=z$ has infinitely many solutions
negative_passages.docid: 151764
negative_passages.text: modular arithmetic, solving $ax + b \equiv c \pmod d$?
negative_passages.docid: 39993
negative_passages.text: Count the number of positive solutions for a linear diophantine equation
negative_passages.docid: 18634
negative_passages.text: Combinations of sets raised to the power of a prime modulus: $\binom{p^{\alpha}-1}k \equiv (-1)^k \pmod p$
negative_passages.docid: 154610
negative_passages.text: Number of solutions for the given equation in finite field of order 32.
negative_passages.docid: 12210
negative_passages.text: Show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$