query: Prove that $ N = \frac{5^{125} - 1}{5^{25} - 1} $ is a composite number.
positive_passages.docid: 143510
positive_passages.text: Prove that $n=\frac{5^{125}-1}{5^{25}-1}$ is a composite number
negative_passages.docid: 75685
negative_passages.text: Prove that there is prime number and natural so $n\times q$ digits are $1$.
negative_passages.docid: 91597
negative_passages.text: How many positive integers $ n$ with $1 \le n \le 2500$ are prime relative to $3$ and $5$?
negative_passages.docid: 111298
negative_passages.text: Direct Proof that $1 + 3 + 5 + \cdots+ (2n - 1) = n\cdot n$
negative_passages.docid: 148713
negative_passages.text: If $p\geq 5$ is a prime number, show that $p^2+2$ is composite.
negative_passages.docid: 6561
negative_passages.text: Prove that the expression $5^{2n+1} \cdot 2^{n+2} + 3^{n+2} \cdot 2^{2n+1}$ is divisible by 19.
negative_passages.docid: 44705
negative_passages.text: Prove that $\frac{1}{a^3(b+c)}+\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)}\ge \frac32$
negative_passages.docid: 91285
negative_passages.text: Prove $a+b+c+d $ is composite
negative_passages.docid: 80242
negative_passages.text: Prove that $n^{2003}+n+1$ is composite for every $n\in \mathbb{N} \backslash\{1\}$
negative_passages.docid: 94209
negative_passages.text: Prove by contradiction that every integer greater than 11 is a sum of two composite numbers
negative_passages.docid: 112512
negative_passages.text: How to prove that there are finitely many $n$ such that $f(1+1/n) = \frac{1}{n+1}$?
negative_passages.docid: 147932
negative_passages.text: How do I prove $n$ is a Carmichael number?
negative_passages.docid: 78726
negative_passages.text: Prove via mathematical induction that $4n < 2^n$ for all $ n≥5$.
negative_passages.docid: 148901
negative_passages.text: Can a composite number $n$ be the arithmetic mean of $\sigma(n)$ and $\varphi(n)$?
negative_passages.docid: 50599
negative_passages.text: Prove that $\frac{1}{1*3}+\frac{1}{3*5}+\frac{1}{5*7}+...+\frac{1}{(2n-1)(2n+1)}=\frac{n}{2n+1}$
negative_passages.docid: 133017
negative_passages.text: Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
negative_passages.docid: 53751
negative_passages.text: Prove that $2^{10}+5^{12}$ is composite