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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?