query: Use strong induction to show that every intger can be expressed as the sum and/or difference of 3's
positive_passages.docid: 150140
positive_passages.text: Show that every nonzero integer has balanced ternary expansion?
negative_passages.docid: 16235
negative_passages.text: Prove by induction that every positive integer is represented by some binary number?
negative_passages.docid: 134202
negative_passages.text: Proof by Induction - Math
negative_passages.docid: 146305
negative_passages.text: Simplify sum of factorials with mathematical induction
negative_passages.docid: 4077
negative_passages.text: Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.
negative_passages.docid: 41784
negative_passages.text: Prove using mathematical induction that $n < 3 ^n$ for all positive integers n.
negative_passages.docid: 42105
negative_passages.text: Fibonacci proof by induction
negative_passages.docid: 123195
negative_passages.text: Prove by induction that a^n+a^-n is an integer.
negative_passages.docid: 88292
negative_passages.text: Prove by induction that $\sum\limits_{i=1}^n \frac{1}{n+i} \leq \frac{3}{4}$
negative_passages.docid: 19129
negative_passages.text: mathematical induction proof of a square vs factorial
negative_passages.docid: 125297
negative_passages.text: Induction to prove $2n + 3 < 2^n$
negative_passages.docid: 151695
negative_passages.text: How to apply induction to this formula?
negative_passages.docid: 962
negative_passages.text: divisibility problem using induction
negative_passages.docid: 17269
negative_passages.text: Strong Induction Proof: Fibonacci number even if and only if 3 divides index
negative_passages.docid: 10976
negative_passages.text: Using induction to prove that $\sum_{r=1}^n r\cdot r! =(n+1)! -1$
negative_passages.docid: 73938
negative_passages.text: Prove that $\sum_{r=1}^nr(r+1)=\frac{n(n+1)(n+2)}{3}$ using induction
negative_passages.docid: 19326
negative_passages.text: What makes induction a valid proof technique?