query: $2^5 \times 9^2 =2592$
positive_passages.docid: 150289
positive_passages.text: A number with an interesting property. $abcd=a^b c^d$
negative_passages.docid: 35326
negative_passages.text: There are infinitely many $N$ such that $\frac{N}{2}$ is a perfect square, $\frac{N}{3}$ is a perfect cube, and $\frac{N}{5}$ is a perfect fifth power
negative_passages.docid: 157771
negative_passages.text: Nested exponent modulus, $2^{2^{517}} \pmod {23}$
negative_passages.docid: 87666
negative_passages.text: Find $n$ such that $n/2$ is a square, $n/3$ is a cube, and $n/5$ a fifth power
negative_passages.docid: 90300
negative_passages.text: Find the remainder when $10^{400}$ is divided by 199?
negative_passages.docid: 75489
negative_passages.text: Solve $x^2$ $mod$ $23 = 7^2$
negative_passages.docid: 45240
negative_passages.text: Starting digits of $2^n$.
negative_passages.docid: 34192
negative_passages.text: Solve $x^{5} \equiv 2$ mod $221\ $ [Taking modular $k$'th roots if unique]
negative_passages.docid: 38156
negative_passages.text: Find the order of $8/9, 14/5,48/28$ in the additive group of $\mathbb{Q}/\mathbb{Z}$
negative_passages.docid: 115284
negative_passages.text: For $5$ distinct integers $a_i$, $1\le i\le5$, $f(a_i)=2$. Find an integer b (if it exists) such that f(b) = $9$.
negative_passages.docid: 153594
negative_passages.text: When is $1^5 + 2^5 + \ldots + n^5$ a square?
negative_passages.docid: 90612
negative_passages.text: Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots
negative_passages.docid: 142135
negative_passages.text: A number with 6 distinct digits which get multiplied by 5 if we move the last digit to front
negative_passages.docid: 84147
negative_passages.text: Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$
negative_passages.docid: 143343
negative_passages.text: The series of reciprocals of the integers that do not contain 9 in their decimal representation
negative_passages.docid: 63416
negative_passages.text: Prove $(n^5-n)$ is divisible by 5 by induction.
negative_passages.docid: 112120
negative_passages.text: Find all primes of the form $2^{2^n} + 5$ for a nonnegative integer n