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Feb
5
revised Prove that a one-color $K_4$ exists in a two-color $K_{18}$
edited body
Feb
5
answered Prove that a one-color $K_4$ exists in a two-color $K_{18}$
Feb
5
comment Prove that a one-color $K_4$ exists in a two-color $K_{18}$
I think we need computers for this.
Feb
5
comment if $r,s$ are rational numbers, then $r+s\sqrt2$ is irrational unless $s=0$?
I personally wouldn't have done it like that, but it is better than what I would have done initially.
Feb
5
comment if $r,s$ are rational numbers, then $r+s\sqrt2$ is irrational unless $s=0$?
it's perfect. ${}{}{}{}$
Feb
5
revised Is $\mathbb{Z}[x]/(x^2 + x + 1, 9)$ isomorphic to $\mathbb{F}_{81}$?
deleted 2 characters in body
Feb
5
answered Is $\mathbb{Z}[x]/(x^2 + x + 1, 9)$ isomorphic to $\mathbb{F}_{81}$?
Feb
4
awarded  Nice Question
Feb
4
awarded  Enlightened
Feb
4
answered Show that there exists c such that $f(c)=c^2$
Feb
4
comment Seeking non-inductive, combinatorial proof of the identity $1^2 + 2^2 + 3^2 + \cdots + n^2 = \frac{n(n + 1)(2n + 1)}{6}$
When $a$ is $1$ there are $1^2$ triples, when $a$ is $2$ there are $2^2$ triples and so on.
Feb
4
awarded  Nice Answer
Feb
4
revised Seeking non-inductive, combinatorial proof of the identity $1^2 + 2^2 + 3^2 + \cdots + n^2 = \frac{n(n + 1)(2n + 1)}{6}$
added 152 characters in body
Feb
4
answered Seeking non-inductive, combinatorial proof of the identity $1^2 + 2^2 + 3^2 + \cdots + n^2 = \frac{n(n + 1)(2n + 1)}{6}$
Feb
3
comment Why Doesn't $2^{1/n}= 1/(2^n)$
$2^{1/n}=\sqrt[n]2$
Feb
3
answered Prove that if $n$ is odd, then $-n$ is odd.
Feb
3
comment Find all cases in which $A \times A$ contains the same number of elements as a given finite set $A$.
what, so you want to describe all finite sets $A$ so that $|A\times A|=|A|$?
Feb
3
comment Which function satisfy $f'(\mathbb{N}) \subseteq \mathbb{N}$
a lot of functions satisfy that, since $\mathbb N$ is not dense we have a ton of continuous extensions for any function $f:\mathbb N \rightarrow \mathbb N$ to all of $\mathbb R$.
Feb
2
answered Inductive factorial formula proof - can't figure out how to finish proof
Feb
2
comment The sum of invertible matrices is also invertible?
did you try at all?