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 2d comment Breaking authentication hard to say without knowing what solver is, but presumably it just finds a solution $\hat x$ to $Ax=b$, which will be the password in the case described. Apr 21 answered Finding the moment generating function of the product of two standard normal distributions Apr 13 comment Checking the boundedness of $A_n = \frac{x}{1-x^2} + \frac{x^2}{1-x^4} + \ldots + \frac{x^{2^n}}{1-x^{2^{n+1}}}$ For which $x$? Consider $n=1$: then the function is unbounded above on $(-\infty, -1)$ and $(-1,1)$ and is obviously negative on $(1,\infty)$ Apr 4 comment Prove, by giving an example , Fermat's Little Theorem Try n=4 and a=2 Apr 2 comment Try to prove: $(A\times B)\cap (C\times D) = (A\cap C)\times(A\cap C)$ Have you written the first displayed equation correctly? Surely you don't mean $A\cap C$ twice on the RHS Mar 30 comment Prove that $n^2+n+41$ is prime for $n<40$ It is true that WLOG $a>0$ for the reason you say. Then either $a^2+ab>0$ and you're done as before, or $a<-b$ in which case $p=a^2+ab+41b^2 \geq a^2 + 40b^2\geq 41$ as neither $a$ nor $b$ can be zero. Mar 30 comment Prove that $n^2+n+41$ is prime for $n<40$ The WLOG at the end doesn't work, because replacing $a,b$ with $-a,-b$ doesn't affect the value of $a^2+ab$. Mar 26 answered Apparent Contradiction to Weyl's Theorem Mar 26 comment Apparent Contradiction to Weyl's Theorem I think you need the span of $v_1-v_3$ as your complement to $W$. For $h\cdot (v_3-v_1)=v_1-v_1=0$ and $f\cdot (v_3-v_1)=v_2-v_2=0$ and $e\cdot (v_1-v_3)=0-0=0$. Mar 26 comment Apparent Contradiction to Weyl's Theorem Why would the span of v3 not being a submodule contradict complete reducibility? Semi simplicity guarantees the existence of a complement, not that that complement is some particular space Mar 18 comment Is it possible to (uniquely) reverse modulo operation by solving multiple equations with the same original integer? Chinese Remainder Theorem Mar 14 comment Extending functions in hyperreals Sin is continuous at zero, so $\sin(\epsilon)$ is infinitely close to $\sin(0)$ Mar 13 comment Analogue of the trivial extension for higher Ext. Your question is a bit confusing. Are you looking for an $n$-extension which represents the zero element of Ext$^n$? There will be lots of them in general, and no obvious reason to prefer one over another. $0 \to A \stackrel{\text{id}}{\to} A \to 0 \to \cdots \to 0 \to B \stackrel{\text{id}}{\to} B \to 0$ is one such. Mar 12 comment Can one cite REU papers written by students? "Allowed" by whom? Mar 12 reviewed Approve A bag contains $4$ red, $6$ white and $2$ blue balls. How many combinations? Mar 12 reviewed Approve Is Sigma $\Sigma$ a mathematical way of doing a for loop? Mar 12 revised Submodules of a product of simple modules added 602 characters in body Mar 12 answered Submodules of a product of simple modules Mar 10 comment Is $\mathbb{Z}[x,y,z]$ an $\mathbb{N}$-graded ring? What is $k$ supposed to be in your answer? Feb 26 awarded Notable Question