Proof by contradiction : $n^3 −n−6 = 0$ means $m^3 − m − 6 ≠ 0$ when $m≠n$
38882
If $n$ is a positive integer such that $n^3 − n − 6 = 0$, then, for every positive integer $m$ with $m \not = n$, $m^3 − m − 6 \not = 0$.
46814
$ a+b+c+d=6 , a^2+b^2+c^2+d^2=12$ $\implies$ $ 36 \leq 4(a^3+b^3+c^3+d^3)-(a^4+b^4+c^4+d^4) \leq48 $
109576
Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$
345
Proving $ \sum _{k=0} ^m \binom nk \binom{n-k}{m-k} = 2^m \binom {n}{m}$.
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
66451
In a ring, how do we prove that a * 0 = 0?
130488
Prove by induction that $3\mid n^3 - n$
20964
Proof that $n^2 < 2^n$
114219
The map $f:\mathbb{Z}_3 \to \mathbb{Z}_6$ given by $f(x + 3\mathbb{Z}) = x + 6\mathbb{Z}$ is not well-defined
47232
Prove $\forall a,b,c \in \mathbb Z$, if $ab+ac\equiv 3\pmod 6$ then $b \not\equiv c \pmod 6$ by contraposition
33052
How to prove $\bar{m}$ is a zero divisor in $\mathbb{Z}_n$ if and only if $m,n$ are not coprime
24601
Proving that a natural number made entirely of 6's and 0's is not a square.
29963
$6$ divides $a+b+c$ if and only if $6$ divides $a^{3}+b^{3}+c^{3}$
134834
$n^2 + (n+1)^2 = m^3$ has no solution in the positive integers
145558
Prove that $2^n+3^n $ is never a perfect square
111938
How do I find a flaw in this false proof that $7n = 0$ for all natural numbers?
5049
Proving $\sum_{k=0}^n(-1)^k\binom nk=0$