query: Find $3^{333} + 7^{777}\pmod{ 50}$
positive_passages.docid: 360
positive_passages.text: Modular exponentiation by hand ($a^b\bmod c$)
negative_passages.docid: 126816
negative_passages.text: Question of remainder on dividing by 7
negative_passages.docid: 94965
negative_passages.text: Solve $x\equiv 1\pmod2$, $x\equiv 2\pmod3$, $x\equiv 3\pmod4$, $x\equiv 4\pmod5$, $x\equiv 5\pmod6$ and $x\equiv 0\pmod7$
negative_passages.docid: 28661
negative_passages.text: What will be the one's digit of the remainder in: $\left|5555^{2222} + 2222^{5555}\right|\div 7=?$
negative_passages.docid: 45882
negative_passages.text: Solving a congruence without Fermat's little theorem
negative_passages.docid: 83634
negative_passages.text: Find $\lim_{n\to \infty}\sqrt[n]{3^n+5^n}$
negative_passages.docid: 144447
negative_passages.text: Show that $504 \mid (n^9 − n^3 )$ for any integer $n$
negative_passages.docid: 46556
negative_passages.text: How to prove $3^{\log_4n} = n^{\log_43}$?
negative_passages.docid: 2137
negative_passages.text: Find the number of ways to express 1050 as sum of consecutive integers
negative_passages.docid: 48053
negative_passages.text: Show that 13 divides $2^{70}+3^{70}$
negative_passages.docid: 72079
negative_passages.text: What are $2222^{5555}+5555^{2222} \pmod 7$ and $9^{2n+1}+8^{n+2} \pmod{73}$?
negative_passages.docid: 96535
negative_passages.text: Show that if $\gcd(a,3)=1$ then $a^7 \equiv a\pmod{63}$. Why is this assumption necessary?
negative_passages.docid: 83935
negative_passages.text: Using congruences, show $\frac{1}{5}n^5 + \frac{1}{3}n^3 + \frac{7}{15}n$ is integer for every $n$
negative_passages.docid: 69858
negative_passages.text: Congruence Equation $3n^3+12n^2+13n+2\equiv0,\pmod{2\times3\times5}$
negative_passages.docid: 17609
negative_passages.text: Finding the remainder of $11^{2013}$ divided by $61$
negative_passages.docid: 17168
negative_passages.text: Find the value of $\sin\frac{2\pi}{7}+\sin\frac{4\pi}{7}+\sin\frac{8\pi}{7}$
negative_passages.docid: 18767
negative_passages.text: How do you find the modular inverse of $5\pmod{\!11}$