query: Find the remainder when $x^{100}$ is divided by $x^2-3x+2$
positive_passages.docid: 156956
positive_passages.text: Give the remainder of $x^{100}$ divided by $(x-2)(x-1)$.
negative_passages.docid: 28330
negative_passages.text: Finding x in $a^{x} \bmod  b = c$ when values a,b, and c are known?
negative_passages.docid: 75141
negative_passages.text: Quotient-Remainder Theorem Proving
negative_passages.docid: 122020
negative_passages.text: What is the remainder when $1! + 2! + 3! +\cdots+ 1000!$ is divided by $12$?
negative_passages.docid: 143368
negative_passages.text: Find the ratio of $\frac{\int_{0}^{1} \left(1-x^{50}\right)^{100} dx}{\int_{0}^{1} \left(1-x^{50}\right)^{101} dx}$
negative_passages.docid: 40896
negative_passages.text: What is the largest positive $n$ for which $n^3+100$ is divisible by $n+10$
negative_passages.docid: 17609
negative_passages.text: Finding the remainder of $11^{2013}$ divided by $61$
negative_passages.docid: 110955
negative_passages.text: Find the coefficient of $x^9$ in $(1+x)(1+x^2)(1+x^3)\cdots(1+x^{100})$
negative_passages.docid: 33105
negative_passages.text: Find the value of $a^2-b^2+c^2$
negative_passages.docid: 2609
negative_passages.text: Is there a quick way to find the remainder when this determinant is divided by $5$?
negative_passages.docid: 128496
negative_passages.text: Find the coefficient of $x^9$ in the expansion of $(1+x)(1+x^2)(1+x^3)...(1+x^{100})$
negative_passages.docid: 133430
negative_passages.text: How to solve $x^x=100$?
negative_passages.docid: 56178
negative_passages.text: X^K+2 split up exponent rules
negative_passages.docid: 5358
negative_passages.text: How to prove that 2017 divides $1^{2017}+2^{2017}+\dots+2017^{2017}$?
negative_passages.docid: 144863
negative_passages.text: Finding integer solutions to $y^2=x^3-2$
negative_passages.docid: 61582
negative_passages.text: Find the remainder of $\frac{2^{2014}}{7}$
negative_passages.docid: 81226
negative_passages.text: Find all integers $a$ for which $x^2-x+a$ divide $x^{13}+x+90$.