query: Prove that (01) and (01...n-1) generate Sn?
positive_passages.docid: 14139
positive_passages.text: $(12)$ and $(123\dots n)$ are generators of $S_n$
negative_passages.docid: 63661
negative_passages.text: integers $n$ such that $(n-1)!+1$ is a power of $n$
negative_passages.docid: 76696
negative_passages.text: Using induction to prove $2^{n-1}(1 + a_1a_2\ldots a_n) \geq (1+a_1)(1+a_2)\ldots(1+a_n)$ for $a_i \geq 1$
negative_passages.docid: 77076
negative_passages.text: Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
negative_passages.docid: 48838
negative_passages.text: Proving the number of $n$ length binary strings with no consecutive $1's$ $b_n$ is equal to $b_{n-1} + b_{n-2}$
negative_passages.docid: 133017
negative_passages.text: Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
negative_passages.docid: 108382
negative_passages.text: Prove $x^n-1$ is divisible by $x-1$ by induction
negative_passages.docid: 72026
negative_passages.text: Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
negative_passages.docid: 424
negative_passages.text: Proving Pascal's Rule : ${{n} \choose {r}}={{n-1} \choose {r-1}}+{{n-1} \choose r}$ when $1\leq r\leq n$
negative_passages.docid: 150156
negative_passages.text: Proving that $S_n$ has order $n!$
negative_passages.docid: 8645
negative_passages.text: A formula for bit strings with no $k$ consecutive $1$'s using generating functions
negative_passages.docid: 16235
negative_passages.text: Prove by induction that every positive integer is represented by some binary number?
negative_passages.docid: 23544
negative_passages.text: Complete induction proof that every $n > 1$ can be written as a product of primes
negative_passages.docid: 111316
negative_passages.text: PROVE if $x \ge-1 $then $ (1+x)^n \ge 1+nx $ , Every $n \ge 1$
negative_passages.docid: 99052
negative_passages.text: Prove that $( 1 + n^{-2}) ^n \to 1$.
negative_passages.docid: 152084
negative_passages.text: Binomial-Theorem proof
negative_passages.docid: 130093
negative_passages.text: Prove by Induction : $n < 2^n$