is there an effective attack against rsa by knowing the coefficient $u$ of the private key?
About integer factorization
What can $E=mc^2$ do? In the famous equation , the variables stand for:     $E$ is energy, $m$ is mass, and $c$ is the speed of light (in vacuum).   And I understand the equation fairly but limited in knowing in its effects/outputs in reality, honestly.   Some example? Could anybody please give me some sort of examples in real world which are done by this equation? Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$ Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$.  Writing out several terms, I think the answer is $1/(n+1)$, but I'm struggling to prove this. I would greatly appreciate it if someone could show how to prove this. How to make an extension function for getting variable or property name like ToString() How do you programmatically set an attribute? Suppose I have a python object x and a string s, how do I set the attribute s on x? So:  &gt;&gt;&gt; x = SomeObject() &gt;&gt;&gt; attr = 'myAttr' &gt;&gt;&gt; # magic goes here &gt;&gt;&gt; x.myAttr 'magic'   What's the magic? The goal of this, incidentally, is to cache calls to x.__getattr__(). Is it possible to spawn mobs in random places? If column matches another file, print every line with match (awk/grep) Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$ I want to show that for $\gcd(a,b) = 1$ $a,b \in Z$   $\gcd(a+b, a-b) = 1$ or $\gcd(a+b, a-b) = 2$ holds.      I think the first step should look something like this:      $d = \gcd(a+b, a-b) = \gcd(2a, a-b)$   From here I tried to proceed with two cases. 1: $a-b$ is even, which leads to $\gcd(a+b, a-b) = 2$ 2: $a-b$ is odd, which leads to $\gcd(a+b, a-b) = 1$  My main problem I think is, that I do not know how I should include $\gcd(a,b) = 1$ in the proof.  Any help is appreciated. Thx in advance. Cherio Woltan According to the official sources, is the radioactive green crystal that serves as Superman's Achilles' heel actually composed of the noble gas krypton, or is it supposed to be made out of some other substance? If so, what is that substance? Frattini subgroup $Φ ( G )$ is not trivial Frattini subgroup $Φ ( G )$ of a group G is the intersection of all maximal subgroups of $G$. The question is  Let $G$ be an abelian group.What is the sufficient and necessary condition of $Φ ( G ) ≠｛e｝$？  I think if $G$ has no torsion part, we cannot say $Φ ( G ) ≠｛e｝$,because $\Bbb Z ×\Bbb Z×・・・ ×\Bbb Z$ has a maximal subgroup $p\Bbb Z ×\Bbb Z×・・・×\Bbb Z$, with intersectioning distinct primes, we gain just a trivial group. So, we need torsion part. But I cannot proceed from here.I only know the answer, $G$ has an element of order $p^2$, that  is, $G$ has theree subgroups. I want to deduce this consequence from steady discussion. P.S  According to this answer, in a ring that is a finite direct product of quotient rings of $\mathbf{Z}$, we can say rattini subgroup is the same as the Jacobson radical of the corresponding ring. I wanted to change my own password (as an admin) so I did the following command:  sudo passwd   and then it prompted for a password but when I tryed to relog, my password was not changed. I'm now wondering what password did I changed since it did prompted me to enter a password but I'm not sure what password did it changed exactly.  I know that if I do sudo passwd &lt;MY_USER&gt; it works, I'm just wondering without a user what happens.  Thank you ANOVA analysis with only mean and standard deviation What should we do with old, very popular closed questions? Motivated by the deletion of     On one hand, I disagree with these closures, because:  These questions were (and still are) very popular They have some good information in them (or at least the first one does) and it feels like bad sportsmanship to remove good information from the internet, particularly when it was contributed by your fellow users  Number 2 in particular bothers me. A lot. On the other hand, I do agree that:  The community of 10k users should be able to decide which closed questions they wish to delete on their own without me intervening These questions should definitely remain closed, because they either have an absurd # of answers, or are duplicates (though some duplicates ). Which means they are eligible for deletion … forever. These questions wouldn't survive more than 10 minutes if asked today on Stack Overflow, so in some ways they are artifacts from the past, like dinosaurs in an era of mammals.  There is some related discussion in:   While I normally favor code solutions here, I am not sure I like the idea that once a question gets 400 upvotes it should become extremely difficult to delete. It feels like mob rule. Official policy on the blog: I was writing a toString() for a class in Java the other day by manually writing out each element of the class to a String and it occurred to me that using reflection it might be possible to create a generic toString() method that could work on ALL classes. I.E. it would figure out the field names and values and send them out to a String.  Getting the field names is fairly simple, here is what a co-worker came up with:  public static List initFieldArray(String className) throws ClassNotFoundException {      Class c = Class.forName(className);     Field field[] = c.getFields();     List&lt;String&gt; classFields = new ArrayList(field.length);      for (int i = 0; i &lt; field.length; i++) {         String cf = field[i].toString();         classFields.add(cf.substring(cf.lastIndexOf(".") + 1));     }      return classFields; }   Using a factory I could reduce the performance overhead by storing the fields once, the first time the toString() is called. However finding the values could be a lot more expensive.  Due to the performance of reflection this may be more hypothetical then practical. But I am interested in the idea of reflection and how I can use it to improve my everyday programming. Is Object constructor called when creating an array in Java? In Java, an array IS AN Object. My question is... is an Object constructor called when new arrays is being created? We would like to use this fact to instrument Object constructor with some extra bytecode which checks length of array being constructed. Would that work? What is $\int_0^1 \frac{\log \left(1-x^2\right) \sin ^{-1}(x)^2}{x^2} \, dx$? formal proof from calulus Given $f:R \to R$, $f$ is differentiable on $R$ and $\lim_{x \to \infty}(f(x)-f(-x))=0$. I need to show that there is $x_0 \in R$ such that $f'(x_0)=0$  I am trying to prove it by contradiction .... so i assume there is no $x_0 \in R$ such that  $f'(x_0)=0$ this means this function is strictly monotonic because the derivative "respects" the mean value theorem so it cannot be negative and positive without passing a zero value ....  (from what i understand the derivative function of a continuous/differentiable functions isn't necessarily continuous but it still respect the mean value theorem i think it's called darboux's theorem )  now from $\lim_{x \to \infty}(f(x)-f(-x))=0$ ,we get $\lim_{x \to \infty}f(x)=\lim_{x \to \infty}f(-x)$  now the last step is the contradiction its very intuitive and even maybe obvious that we can't get $\lim_{x \to \infty}f(x)=\lim_{x \to \infty}f(-x)$ for strictly monotonic function but i cant think of a formal way to prove it . I am trying to make a pirate ship and am trying to attach rope to the sails. my rope is made using a path, and soft body physics. I can not find a way to attach my rope to the sail. and I can not use pinned vertices because this is not a cloth modifier. How to add line break to caption without using caption package I wish to add a line break to a caption, but I would wish to avoid adding of caption package. Is it possible?  \documentclass{article} \usepackage[format=plain,  justification=raggedright,singlelinecheck=false]{caption} \begin{document} \begin{figure} \caption{This is the caption\\ This is the second line} \end{figure} \end{document} Consider a block cipher with a key of size 128 bits but a small block size, say 32 bits.  Is this kind of block cipher secure?  I would like to know to what extent I can use a small block cipher, like a 32 bit block cipher. What are the constraints so that the use is acceptable in a real life application.  For instance, if we use a one-time key, that is, to encrypt only one message. Besides, the message could be small.  Suppose that when we want so send one file, we perform a key agreement so that we use the key for one message. This scenario is not efficient, but the CPA find-then-guess game is not adequate in this case. Show that $\sum_{n = 1}^\infty n^qx^n$ is absolutely convergent, and that $\lim_{n \rightarrow \infty}$ $n^qx^n = 0$ I'm having trouble with proving the following for my math study:  Let $x$ be a real number with $|x| &lt; 1$, and $q$ be a real number. Show that the series $\sum_{n = 1}^\infty n^qx^n$ is absolutely convergent, and that $\lim_{n \rightarrow \infty}$ $n^qx^n = 0$  I tried this:  $\sum_{n = 1}^\infty n^qx^n$ = $x + 2^q + 3^qx^3 + ...$ $= x(1 + 2^qx + 3^qx^2 + ...)$  So far, I don't know how I have to do this, I tried to apply the root test on this, but for that I would need to compute the lim sup of the series, so I thought that was not correct. Could you explain me how to prove this?  Thanks in advance!