query: Find the remainder when $10^{20^{30}}$ is divided by $23$
positive_passages.docid: 360
positive_passages.text: Modular exponentiation by hand ($a^b\bmod c$)
negative_passages.docid: 100336
negative_passages.text: Find an integer having the remainders $2,3,4,5$ when divided by $3,4,5,6$, respectively.
negative_passages.docid: 97150
negative_passages.text: Solve $[2^{(2^{403})}] = [a]$ in $\mathbb Z_{23}$ where $0 \le a < 23$.
negative_passages.docid: 32381
negative_passages.text: How to calculate $276^{246} \mod 323$ without a calculator?
negative_passages.docid: 151692
negative_passages.text: When does $2^n-1$ divide $3^n-1$?
negative_passages.docid: 117167
negative_passages.text: $3^{n+1}$ divides $2^{3^n}+1$
negative_passages.docid: 146203
negative_passages.text: if p is prime then 1920 divides $p^4-10p^2+9$
negative_passages.docid: 49967
negative_passages.text: Find the last two digits of $ 7^{81} ?$
negative_passages.docid: 136300
negative_passages.text: {5,15,25,35} is a group under multiplication mod 40
negative_passages.docid: 103274
negative_passages.text: Integer solutions to the equation $a^3+b^3+c^3=30$
negative_passages.docid: 36031
negative_passages.text: Finding modular of a fraction
negative_passages.docid: 92760
negative_passages.text: What is the mathematical symbol/representation for the remainder operation?
negative_passages.docid: 5037
negative_passages.text: Find the last two digits of $3^{45}$
negative_passages.docid: 126816
negative_passages.text: Question of remainder on dividing by 7
negative_passages.docid: 107008
negative_passages.text: Find the remainder when $45!$ is divided by $47$?
negative_passages.docid: 151636
negative_passages.text: Fast way to calculate n! mod m where m is prime?
negative_passages.docid: 17766
negative_passages.text: Find $n^{th}$ term of $\frac23,\frac35,\frac58,\frac8{13}\dots$