query: Weak Mathematical Induction for Modulo Arithmetic $8\mid 3^{2n}-1$
positive_passages.docid: 31074
positive_passages.text: Mathematical Induction divisibility $8\mid 3^{2n}-1$
negative_passages.docid: 360
negative_passages.text: Modular exponentiation by hand ($a^b\bmod c$)
negative_passages.docid: 68308
negative_passages.text: A (probably trivial) induction problem: $\sum_2^nk^{-2}\lt1$
negative_passages.docid: 141704
negative_passages.text: Fractional exponentiation in modular arithmetic
negative_passages.docid: 25496
negative_passages.text: Avoiding proof by induction
negative_passages.docid: 31900
negative_passages.text: Induction on Real Numbers
negative_passages.docid: 55428
negative_passages.text: Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
negative_passages.docid: 91896
negative_passages.text: Induction (Geometric sequence)
negative_passages.docid: 42285
negative_passages.text: Prove by mathematical induction.
negative_passages.docid: 65742
negative_passages.text: Strong Induction: Every natural number $n\geq 8$ can be represented as $n=3k + 5\ell$
negative_passages.docid: 33757
negative_passages.text: For what natural numbers is $n^3 < 2^n$? Prove by induction
negative_passages.docid: 18301
negative_passages.text: Proof by Induction involving Inequality and Factorials as denominators
negative_passages.docid: 122019
negative_passages.text: Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}$
negative_passages.docid: 154133
negative_passages.text: Flawed proof by induction that $a^{n-1}=1$
negative_passages.docid: 57846
negative_passages.text: Multiplicative inverse in $\operatorname{GF}(2^8)$?
negative_passages.docid: 125220
negative_passages.text: Solving binomial theorem via induction
negative_passages.docid: 137012
negative_passages.text: Mathematical Induction for Recurrence Relation