query: Show that $x^8 \equiv 1 \pmod{32}$
positive_passages.docid: 152039
positive_passages.text: Prove that $a^{2^n}=1 \mod 2^{n+2}$
negative_passages.docid: 7414
negative_passages.text: Prove that odd perfect square is congruent to $1$ modulo $8$
negative_passages.docid: 40892
negative_passages.text: How to solve a linear congruence $8n+9\equiv 0\pmod{\!1163}$
negative_passages.docid: 51153
negative_passages.text: Number of solutions to $x^2\equiv a\pmod m$
negative_passages.docid: 108237
negative_passages.text: Show $a^p \equiv b^p \mod p^2$
negative_passages.docid: 32762
negative_passages.text: Proof for: $(a+b)^{p} \equiv a^p + b^p \pmod p$
negative_passages.docid: 15897
negative_passages.text: Solve a congruence $1978^{20}\equiv x\pmod{125}$
negative_passages.docid: 39266
negative_passages.text: Show that $\tan {\pi \over 8} = \sqrt 2 - 1$
negative_passages.docid: 127901
negative_passages.text: If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$
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: 29231
negative_passages.text: Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
negative_passages.docid: 4972
negative_passages.text: Mod of numbers with large exponents [modular order reduction]
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: 108385
negative_passages.text: Irreducible factors of $x^8 - x$ in $Z/2Z[x]$
negative_passages.docid: 127945
negative_passages.text: Number of solutions to the congruence $x^q \equiv 1 \mod p$.
negative_passages.docid: 102432
negative_passages.text: Irreducible polynomial of degree $8$
negative_passages.docid: 77816
negative_passages.text: Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.