Prove or disprove that $n^3-n$ is divisible by $6$, without using induction
100892
Proving divisibility of $a^3 - a$ by $6$
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
108382
Prove $x^n-1$ is divisible by $x-1$ by induction
65430
Using the Well Ordering Principle to Show that n^3 - n is divisible by 6.
42526
The product of $n$ consecutive integers is divisible by $ n!$ (without using the properties of binomial coefficients)
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
122577
Prove that $(n^3 - 1)n^3(n^3 + 1)$ is divisible by $504$
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
21100
Simple Proof by induction: $9$ divides $n^3 + (n+1)^3 + (n+2)^3$
122711
Prove by induction that $n^3 + 11n$ is divisible by $6$ for every positive integer $n$.
125297
Induction to prove $2n + 3 < 2^n$
91921
Divisibility of $n\cdot2^n+1$ by 3.
136700
Proving divisibility of expression using induction
49096
How can I prove $5^{3^n}+1$ is divisible by $3^{n+1}$
86479
How to Prove with Mathematical Induction $3^n > n^2$
128306
Show that for all $n ∈ Z$, $2n^3 + 3n^2 + n$ is divisible by both 2 and 3.