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Apr
26
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