query: find the smallest positive multiple $n$ of 1994 such that the produc of the divisors of $n$ is $n^{1994}$
positive_passages.docid: 27449
positive_passages.text: Product of Divisors of some $n$ proof
negative_passages.docid: 134159
negative_passages.text: Smallest value of $a^2 + b^2 + c^2+ d^2$, given values for $(a+b)(c+d)$, $(a+c)(b+d)$, and $(a+d)(b+c)$
negative_passages.docid: 140144
negative_passages.text: Can you find an element of order 10 in $\mathbb{Z}_{31}^{*}$
negative_passages.docid: 133481
negative_passages.text: How to find the smallest number with just $0$ and $1$ which is divided by a given number?
negative_passages.docid: 108238
negative_passages.text: Find the smallest integer $n$ greater than $1$ such that the last $3$ digits of $n^2$ are the same as the last $3$ digits of $n$.
negative_passages.docid: 48655
negative_passages.text: Find all n such that : $3 \mid (n2^{n}+1)$
negative_passages.docid: 34440
negative_passages.text: Finding Value of the Infinite Product $\prod \Bigl(1-\frac{1}{n^{2}}\Bigr)$
negative_passages.docid: 90806
negative_passages.text: Find all positive integers $n$ such that $n$ is divisible by all the positive integers less than or equal to $\sqrt{n}$
negative_passages.docid: 39953
negative_passages.text: $a\mid b,\ c\mid d\,\Rightarrow\ ac\mid bd $ $\ \, \bf\small [Divisibility\ Product\ Rule]$
negative_passages.docid: 110444
negative_passages.text: Finding out the number of divisors
negative_passages.docid: 149249
negative_passages.text: Beginner: How to complete the induction case in a proof that all multiples are a product of the least common multiple
negative_passages.docid: 84491
negative_passages.text: Finding the smallest positive integer $n$ such that $S_n$ contains an element of order 60.
negative_passages.docid: 137175
negative_passages.text: Fermat's little theorem proof by Euler
negative_passages.docid: 157186
negative_passages.text: Finding integers satisfying $m^2 - n^2 = 1111$
negative_passages.docid: 126367
negative_passages.text: Let $p$, $q$ be prime numbers such that $n^{3pq} – n$ is a multiple of $3pq$ for all positive integers $n$. Find the least possible value of $p + q$.
negative_passages.docid: 68233
negative_passages.text: Fermat's little theorem's proof for a negative integer
negative_passages.docid: 33052
negative_passages.text: How to prove $\bar{m}$ is a zero divisor in $\mathbb{Z}_n$ if and only if $m,n$ are not coprime