query: For $a,b>2$, $a,b\in \Bbb{N}$ , prove that $2^a+1$ is never divisible by $2^b-1$
positive_passages.docid: 26940
positive_passages.text: $2^a +1$ is not divisible by $2^b-1$.
negative_passages.docid: 106981
negative_passages.text: Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$
negative_passages.docid: 130093
negative_passages.text: Prove by Induction : $n < 2^n$
negative_passages.docid: 33996
negative_passages.text: Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
negative_passages.docid: 139503
negative_passages.text: How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
negative_passages.docid: 110695
negative_passages.text: Divisor of $2^{2^n} + 1$ modulus $2^{n+1}$
negative_passages.docid: 112031
negative_passages.text: Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
negative_passages.docid: 68328
negative_passages.text: Infinitely many $n$ such that $2^n-n$ is divisible by a prime
negative_passages.docid: 52644
negative_passages.text: Prove $2^k+1$ divisible by 3 for odd K
negative_passages.docid: 98963
negative_passages.text: Prove that neither $A$ nor $B$ is divisible by $5$
negative_passages.docid: 99631
negative_passages.text: Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$
negative_passages.docid: 91921
negative_passages.text: Divisibility of $n\cdot2^n+1$ by 3.
negative_passages.docid: 30134
negative_passages.text: For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
negative_passages.docid: 127720
negative_passages.text: Prove that $\bigcup_{n \in \Bbb{N}} [1/n,1] = (0,1]$.
negative_passages.docid: 100305
negative_passages.text: Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
negative_passages.docid: 48333
negative_passages.text: Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
negative_passages.docid: 136304
negative_passages.text: Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$