query: Proving divisibility by using induction: $133 \mid (11^{n+2} + 12^{2n+1})$
positive_passages.docid: 15631
positive_passages.text: Show that $11^{n+1}+12^{2n-1}$ is divisible by $133$.
negative_passages.docid: 40692
negative_passages.text: Proving by strong induction that $\forall n \ge 2, \;\forall d \ge 2 : d \mid n(n+1)(n+2)...(n+d-1) $
negative_passages.docid: 100305
negative_passages.text: Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
negative_passages.docid: 10629
negative_passages.text: How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction
negative_passages.docid: 157294
negative_passages.text: Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
negative_passages.docid: 85941
negative_passages.text: Proof by induction that $n^3 - n$ is divisible by $6$
negative_passages.docid: 59135
negative_passages.text: What is the proof of divisibility by $13$?
negative_passages.docid: 147140
negative_passages.text: Prove the divisibility test by $7,11,13$ for numbers more than six digits
negative_passages.docid: 87379
negative_passages.text: How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
negative_passages.docid: 125297
negative_passages.text: Induction to prove $2n + 3 < 2^n$
negative_passages.docid: 12729
negative_passages.text: Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
negative_passages.docid: 106847
negative_passages.text: Proof that $n^3+2n$ is divisible by $3$
negative_passages.docid: 100080
negative_passages.text: Proving with induction $(1-x)^n<\frac 1 {1+nx}$
negative_passages.docid: 74523
negative_passages.text: Proof by Cases involving divisibility
negative_passages.docid: 91921
negative_passages.text: Divisibility of $n\cdot2^n+1$ by 3.
negative_passages.docid: 139776
negative_passages.text: Divisibility tests and remainder mod $9,11,99,101,999,1001\,$ (casting out nines and elevens)
negative_passages.docid: 26336
negative_passages.text: Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$