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I want to know if there is another way to solve the equation:  $$(x+1)^y-x^z=1$$  for positive integers $x,y,z$ greater than $1$ without using the Catalan identity. Does exist? By now I only know that $x\mid y$. I have seen people showing one slide progressively by pressing Enter. Could anyone tell me how to realize that in Beamer? I'm trying to use the Bash parameter expansions to modify the output of a command substitution or another parameter expansion. The following nested expansions work quite well in Zsh; but result in a &quot;bad substitution&quot; error in Bash: ${${PWD##*/}//trunk/latest}  or ${$(basename $PWD)//trunk/latest}  the output should be the last folder of the $PWD, replaced by latest when my current directory is trunk so /home/user/trunk should become latest Is there a Bash equivalent allowing to chain expansions without relying on variables or pipes? Or do Bash expansions only allows the input to be a string or a plain variable? What is the purpose of the word 'self'? I have the following page (deadlink: http://www.workingstorage.com/Sample.htm ) that has a footer which I can't make sit at the bottom of the page. I want the footer to  stick to the window bottom when the page is short and the screen is not filled, and stay at the document end and move down as normal when there is more than a screenful of content (instead of overlapping the content).  The CSS is inherited and befuddles me. I can't seem to change it properly to put a minimum height on the content or make the footer go to the bottom. How to input integer value to an array, based preceeding row + column values? Eigen Values Proof a.) Let A and B be $n$ x $n$ matrices. Prove that the matrix products   $AB$  and $BA$ have the same eigenvalues.      b.) Prove that every eigenvalue of a matrix A is also an eigenvalue of   its transpose $A^T$. Also, prove that if v is an eigenvector of A with   eigenvalue $\lambda$ and w is an eigenvector of $A^T$ with a different   eigenvalue $\mu \ne \lambda$, then v and w are orthogonal vectors with   respect to the dot product.   For a, I know that if their eigenvalues are the same then their eigenvectors must relate too.    For the first part of b, is it similar to proving that the $det(A) =det (A^T)$? And, I do not know how to do the second part. What is a single word for a person who, as a habit, exaggerates a lot when relating information?   So for example, they relate something that happened but exaggerate so much that they are including clear falsehood and they are well known for doing that. Can others in my party go through TSA PreCheck? If I have  (i.e. I have a KTN from TSA and the "pre-check" logo gets printed on my boarding pass) and a travel companion does not, can they go with me through the PreCheck security lines? This is assuming that the travel companion is booked in the same reservation on the same flights and is also a U.S. citizen and not on any no-fly or otherwise increased scrutiny lists.  I'm guessing the answer is no, but I haven't seen anything from TSA specifically addressing this. Can an irrational number raised to an irrational power be rational? Can an irrational number raised to an irrational power be rational?  If it can be rational, how can one prove it? Nice proofs of $\zeta(4) = \frac{\pi^4}{90}$? Prove that:$\int_{a}^{b} f(x) dx = b \cdot f(b) - a \cdot f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) dx$ Find the general solution of $xy''-(1+x)y'+y=x^2$ knowing that the homogeneous equation has the following solution: $e^{ax}$, where $a$ is a parameter you have to find.  I have found that $a=1$ or $a=1/x$. What is the probability of a biased coin coming up heads given that a liar is claiming that the coin came up heads? A biased coin is tossed.   Probability of Head - $\frac{1}{8}$  Probability of Tail - $\frac{7}{8}$  A liar watches the coin toss. Probability of his lying is $\frac{3}{4}$ and telling the truth is $\frac{1}{4}$. He says that that the outcome is Head. What is the probability that the coin has truly turned Head?  My Attempt:  I used the formula: $$P(A \mid B) = \frac{P(A\cap B)}{P(B)}$$  $\ \ \ \ \ \ $P(it is head GIVEN liar said it's head) = P(it's head AND liar said it's head) / P(liar said it's head)  or, P(it is head GIVEN liar said it's head) = $\frac{ \frac{1}{8} \frac{1}{4} }{ \frac{7}{8}\frac{3}{4} + \frac{1}{8}\frac{1}{4} }$ [using a probability tree will be helpful here]  or, P(it is head GIVEN liar said it's head) = $\frac{1}{22}$  The Question: Is the method I used wrong in any way? Some others I have talked to are saying the answer will be $\frac{1}{4}$. Their reasoning is this: since the liar lies 3 times out of 4 and he said it is head, then the probability of it being head is 1/4. So who is right? What will be the answer? 1 Plot, 2 Scale/Axis I had opened a terminal to install macchanger via sudo apt-get install -y macchanger, and then entered my password. It stated that macchanger was already the newest version, so I typed clear and then ran:  sudo ifconfig eth0 down   which is when this error message appeared:  eth0 ERROR while getting interface flags: no such device   This is a laptop and I am connected via ethernet cable.  How can I resolve this, so that I can run macchanger?    So I used ifconfig -a and I'm looking but seeing no mention of  eth0  The interfaces that are showing top to bottom are:  enp58s0f1 lo tun0 UNSPEC wlp59s0   The only reference to ethernet is the MAC and also txqueuelen   Does this help in figuring what I need to do to get this sorted? I just ran into the problem of embedding fonts while trying to publish with lulu.com. Although everyone apparently is 'supposed' to handle those 35 standard fonts for some strange reason they won't accept pdf's without them included. So one way that according to  is supposed to work (I haven't tried yet, but hopefully it does work) is to convert the pdf to ps and then back to pdf and include the fonts at that time:  pdftops file.pdf ps2pdf14 -dPDFSETTINGS=/prepress file.ps   But this feels at least to me like the wrong way of doing things. Is there some way of passing the parameter directly to pdflatex to tell it to embed those fonts?   And, if not -- How do we go about getting such a feature? (Because it can't only be me who has this sort of problems) How to disable the physical sim and only use the eSIM on iPhone XS/iPhone XS Max? I'm wondering if there is a way to turn off the Physical sim and use only the eSim on my iPhone XS Max. I travel a lot and I'm loving the use of eSIM.   I understand that I can turn off the eSIM if its required, but I wanted to know if there was any way to turn the Physical Sim off and leave only the eSim ON.  Note - I have an unlocked iPhone XS Max. What's the function of the ~ bitwise operator (Tilde) Understanding DNA match of 1,723 cM I have a DNA match of 1,723 cM with a male 6 years younger than me. His father is one of a twin, could my match be not my half-sibling but my 1st cousin.