Prove the following statement using the contrapositive method. If $ n^2 $ is divisible by 3 then n is divisible by 3.
50534
Prove that if $n^2$ is divided by 3, then also $n$ can also be divided by 3.
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
128306
Show that for all $n ∈ Z$, $2n^3 + 3n^2 + n$ is divisible by both 2 and 3.
22073
Prove by induction that $n^2<n!$
50663
prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$
67527
Proof by Induction that $3^n ≥ 1+2^n$
33757
For what natural numbers is $n^3 < 2^n$? Prove by induction
34767
Proving $\left(1+\dfrac{1}{1^3}\right)\left(1+\dfrac{1}{2^3}\right)\cdots\left(1+\dfrac{1}{n^3}\right)<3$ for all positive integers $n$
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
49299
Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
10191
Binomial theorem: divisibility by $n^2$
81377
Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$
63416
Prove $(n^5-n)$ is divisible by 5 by induction.
114867
Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
55273
Prove by mathematical induction that: $\forall n \in \mathbb{N}: 3^{n} > n^{3}$
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.