query: What's the digit sum of $4444^{4444}$?
positive_passages.docid: 853
positive_passages.text: Write down the sum of sum of  sum of digits of $4444^{4444}$
negative_passages.docid: 101017
negative_passages.text: What is the sum of $\sum\limits_{i=1}^{n}ip^i$?
negative_passages.docid: 116379
negative_passages.text: What are the last two digits of $2017^{2017}$?
negative_passages.docid: 28957
negative_passages.text: Verifying that $2^{44}-1$ is divisible by $89$
negative_passages.docid: 67312
negative_passages.text: How to find the last digit of $3^{1000}$?
negative_passages.docid: 144779
negative_passages.text: The number of ways to represent $(n^2+n)/4$ as a sum of $n/2$ distinct integers in $1,\dots,n$
negative_passages.docid: 108919
negative_passages.text: Numbers till 400 divisible by 2, 3, 5, 7
negative_passages.docid: 54441
negative_passages.text: Last two digits of $3^{400}$
negative_passages.docid: 4475
negative_passages.text: Find the remainder when $2^{2016}$ is divided by $47$
negative_passages.docid: 12760
negative_passages.text: The last 2 digits of $7^{7^{7^7}}$
negative_passages.docid: 151375
negative_passages.text: There are $3$ Zero-Sum Numbers!
negative_passages.docid: 112253
negative_passages.text: How to find sums like $\sum_{k=0}^{39} \binom{200}{5k}$
negative_passages.docid: 49116
negative_passages.text: Finding the last digit of $103^{103^{103^{103^{103}}}}$
negative_passages.docid: 151179
negative_passages.text: Finding the value of $\sum k/3^k$
negative_passages.docid: 110996
negative_passages.text: Sum of the form $r+r^2+r^4+\dots+r^{2^k} = \sum_{i=1}^k r^{2^i}$
negative_passages.docid: 94871
negative_passages.text: Sum of an unorthodox infinite series
negative_passages.docid: 70492
negative_passages.text: What is the shortest way to compute the last 3 digits of $17^{256}$?