query: Find $ \ \ 8^{504} \equiv \pmod 5$
positive_passages.docid: 360
positive_passages.text: Modular exponentiation by hand ($a^b\bmod c$)
negative_passages.docid: 119433
negative_passages.text: How to find modulo of large numbers like $9801\! \pmod {\!32}$
negative_passages.docid: 9039
negative_passages.text: What is the best way to solve modular arithmetic equations such as $9x \equiv 33 \pmod{43}$?
negative_passages.docid: 75166
negative_passages.text: Find with proof all positive integers $n$ such that $2^n + 1 \equiv 0 \pmod{n}$
negative_passages.docid: 111555
negative_passages.text: Find $a,b \in \mathbb{N}$ with $\mathrm{lcm}(a,b)=12\gcd(a,b)\,$ and $\,a\bmod b = 5$
negative_passages.docid: 77448
negative_passages.text: $n\ge 8\,\Rightarrow\, n = 3j + 5k\ $ for $\,j,k,n\in \Bbb N$
negative_passages.docid: 95033
negative_passages.text: Find the remainder of a number with a large exponent
negative_passages.docid: 22029
negative_passages.text: Solving modular arithmetic questions
negative_passages.docid: 157771
negative_passages.text: Nested exponent modulus, $2^{2^{517}} \pmod {23}$
negative_passages.docid: 60305
negative_passages.text: Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$
negative_passages.docid: 79219
negative_passages.text: Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
negative_passages.docid: 124995
negative_passages.text: $p\equiv 1,2,3\text{ mod }8 \Rightarrow p=a^2+2b^2\text{ for some $a,b\in\mathbb{Z}$.}$
negative_passages.docid: 66703
negative_passages.text: Show that $8 \mid (a^2-b^2)$ for $a$ and $b$ both odd
negative_passages.docid: 34192
negative_passages.text: Solve $x^{5} \equiv 2$ mod $221\ $ [Taking modular $k$'th roots if unique]
negative_passages.docid: 109490
negative_passages.text: Modular arithmetic problem (mod $13$)
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: 41673
negative_passages.text: Solve congruence system $\ x\equiv m_i-1 \pmod{m_i}\,$ for $\,i = 1,\ldots, k$