Prove by induction that $3\mid n^4-n^2$ for all $n \in \mathbb{Z^+}$, $n\ge2$.
48875
$n^3 \equiv n^5 \pmod{12} $?
8609
Prove by induction that $n!>2^n$
125297
Induction to prove $2n + 3 < 2^n$
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
153123
Proving by induction $4^n  0$
52930
Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
139269
Prove that $2n-3\leq 2^{n-2}$ , for all $n \geq 5$ by mathematical induction
90835
Use induction to prove that $2^n \gt n^3$ for every integer $n \ge 10$.
71451
A proof by strong induction that $a_n\le3^n$ where $a_n=a_{n-1}+a_{n-2}+a_{n-3}$
27580
Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$
49299
Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
119118
Prove $n\mid \phi(2^n-1)$
62177
Prove that: $2^n < n!$ Using Induction
44906
Use induction to prove that $2^n$ divides $(2n)!$ for any $n\in\mathbb{Z}_{\geq0}.$
61117
Prove by induction: $n! \ge 2^{(n-1)}$ for any $n \ge 1$