Can Sum of a Rational Number and Its Reciprocal Be an Integer?
So $fracmnfracnmfracm^2n^2mn$ an integer. This means $$m^2-n^2 mod mn $$ $$m^2n^2kmn$$ for some integer $k$.If $k1$, then $(mn)(m-n)0$ so $mn$ or $m-n$.With some calculus, it is best shown properties about its zeros, the equation $x^2y^2zxy$. But there are no zeros outside of cases where $m,n0; mn; m-n$â¢ Related QuestionsCan we simulate FPGA board?I believe what you are talking about is having a Test Bench, a virtual environment used to verify a design. It can be done with any simulation software, like Multisim. You can either code a virtual approximation of what your inputs and outputs are in Multisim/etc. and have your FPGA simulation interact with it, if you're lucky this may already exist and you just have to find it------Email sent from server with rDNS & SPF being blocked by Hotmailok so for understanding. You want send an email from your google account email@example.com with an other FROM adress? Something like firstname.lastname@example.org?But when your server send direct the mail over sendmail for example and you know that they don't come to the other site check the mail log if you have access. There you can see the complete connection to the other site------cat-like program duplicateI couldn't get it to fit in 100 bytes, but it is assembly. Eight bytes could be saved at the cost of changing the return status to 1 instead of 0:Now, if you really want 100 bytes, here is one in exactly 100 bytes. The problem is that it doesn't exit correctly, it just segfaults:The instructions say to only use standard libraries; is there extra credit for using no libraries at all?.------scoping a UART interfaceThe serial BT module can be checked easily without any tools. Short TX to RX then pair the module with a phone, PC, etc., open a terminal and type something. If module is working you'll get echo back. Make sure 'local echo' is turned off in the terminal. If you have known good module practice on it first.FTDI USB to serial can be tested using the same technique.------What is my training score the mean_train_score or mean_test_score?The mystery retains inside working of K-fold cross validation, which actually divides the whole data into train and test data K number of times in a specific ratio. For more about it's working please refer herethe mean score calculated on the training set is mean_train_score and on the testing set is mean_test_score.According to your question your training score should be: mean_train_error------When is it OK not to have dedicated testers/QA team?In this case my guess is your product is used by such tech savy users that you get plenty of feedback when problems do pop up. And CBA said it isn't mission critical.As long as your developers continue to do a good job & you are willing to take feedback from users it seems to be a model that works for you so why tinker with a good thing?------ANOVA results do not match post-hoc Tukey test, how to proceed?It's possible that you could have no significant differences among all of the individual means with the most liberal of testseven a planned comparison. I was just tasking my students to develop simulated data with just this feature.You do an ANOVA to test the pattern of your data. If the test is passed then, in most situations, all you need to do is then describe that pattern------How to set local_listener to null upon creating databaseI tested specifying -initparams local_listener'' but the local_listener has been set anyways by specifying the empty string.You might want to create a custom template referencing a .sql script with the command alter session set local_listener.I'd only make that effort if in need to use it multiple times, though. If it is a one time thing, maybe you're better off setting local_listener manually------Facebook Links being blocked from previewThe Facebook Sharing Debugger is the tool you want - you need to be logged in to Facebook to use it.This will allow you to test a URL, and see both what Facebook has cached, and request an updated scrape:You can also submit a list of URLs that you'd like to be invalidated from the Cache so that you can refresh a bunch of pages if required------Can adjuncts be arguments?If you "hear that only complements and specifiers can contain the argument for a verb" ... well, that's really a matter between you and your syntax confessor. Not everybody believes that this is true, however, or even useful. Three-place predicates typically have, well, three arguments. In English,These verbs often govern the Dative Alternation, syntactically:One really can't expect to read this all off one PS marker, however cheerfully decorated------Creating a script to show a notification when updates are availableOn debian based distribution you can use the pk-update-icon package:Displays an update-notification tray iconThis small tool displays notifications and an icon in the tray area of the panel when package updates are available. It is primarily designed for desktops which do not already have this functionality integrated, such as Xfce.Schedule a cron job (a brief delays is used for testing propose.) e,g:past the following line:.------How do I control a servo using a beaglebone black running ubuntuIt's python but easy to install: Otherwise you can fopen files in the device tree and write to them, or you can open /dev/mem and directly access the registers for the PWM drivers.I strongly recommend using the first method it is far easier than the third and basically the same as the second just far more tested and probably well written------With sudoers, how can I allow a user to change the group of files/folders within their home directory?You might be best off writing a script and enabling that in sudoers. If your users will only ever need to run it on * within their homedir then something as simple as the following. It makes use of the SUDO_USER environment variable which you can find out more about here: sudo.ws/sudo/sudo.man.html#environmentI haven't tested this but it should work in principal------How to monitor freeradius using EAP-MSCHAP v2 authentication method with Nagios?I have nagios setup to monitor radius, if I remember right all that is required is to have the servers defined in /etc/radiusclient/servers and then..then use that as a check_command like any other service.This has the password in the config file and on the commandline, but if you have a dedicated nagios box and test user like me this isn't much of an issue.------Delivery is delayed errors, seems specific to Office 365 recipientsWith the current detail, it's a guess, but I seen report that from Office 365 some enterprise got problem to receive their mail because on how the email is sent, as some router / antispam feature on your side can badly close the connection. Like that KB for Cisco ASA, that when inspection is On it fail; html.------How DApp actually talks to Ganache ethereum node?Metamask uses web3 to talk to Ethereum nodes. Metamask also injects the web3 into the browser for any application running to use to connect to a node (selected in metamask by the user). Metamask has the user generated private keys in browser storage which when the user agrees are used to sign any transaction that can be submitted to the nodes. The signing, sending etc. are done using web3.------Is this normal that www-data still needs to have read and execute permissions on htdocs when using PHP-FPM?Show us the way you have connected php-fpm and apache, there's certainly some Directory -- or such -- instructions on the Apache side , or maybe you've used mod_proxy_fcgid?If not then Apache is quite certainly forbidding the access before any fastcgi task gets tested. Using debug log level in Apache could certainly show the difference between the request with apache access allowed on the directory and without------Network problem EA gamesIf the game is crashing the network, it is possible that the drivers are out of date OR the software used in the game is conflicting with his native drivers and causing a crash. My PC crashes a certain program whenever I plug my headphones in, as an example.Things to try would include:Unfortunately, there is no one-stop shop answer to solve this, just some testing. Good luck.------How to use xcopy to copy directories with specific prefix to another folderI managed to accomplish this with xcopy, dir /b and for in simple scenarios, but when I set up a complex test, it failed. xcopy is simply too old and outdated.I recommend using PowerShell instead. The following PowerShell command gives you what you want.In fact, I advise ditching Command Prompt and batch files altogether. They belong to 1990s. PowerShell and its .ps1 are the way to go.------When is a good time to develop new automated GUI tests in an existing application still under development?GUI features are dependant on underlying DB, Services, Business logic. Before the gui is stabilized you can focus on automating services, db layer. This would help you focus on sub-systems. Also, when you need to do End to End tests, example- GUI - Service - DB level tests it would help reuse those validations.I would recommend GUI automation when the underlying services, DB, business logic are stable / implemented------PHP - exploiting a user input function parameter in eval() closedThis is very bizarre construct but it's not the first time someone is using eval for template engine.It doesn't look to be exploitable from what is shown here because $_GET'in' is not passed to eval. What is passed to eval() is the result from template().Maybe there's something inside template which would allow for code execution, but it's not there so there's no way to test it------Where are Champernowne's zeroes?Does the same as other answers -- takes the range from 0 to input $n, -joins together into a string, takes the $n index, checks if it's -equal to 48 (i.e., ASCII for 0).Note this will only work up to input 49999, as the PowerShell range operator .. only supports ranges of 50,000 elements or fewer. For larger inputs, you'll need to use the following, based on my previous Champernowne answer, at 58 bytes:------Is there a way to remove files from a folder that are in another folder?Using bashSure you could be more more safe by checking if the file is there, or checking if the filename is safe. But assuming you just want to get this done, and don't have any ridiculously named files in folderB - this is a quick and dirty way to get it done.(and you can use the bash emulator that comes with git, if you aren't running Win10 bash)------How to test whether next token on input stream is catcode 10Use futurelet. It's a TeX primitive, and it's the only way to do this sort of thing. In fact, that's why it was introduced.The LaTeX 3 stuff uses futurelet under the hood, and to my way of thinking makes things more complicated and considerably slower.If you understand this you can solve the problem yourself (except perhaps for the problem of getting a space token into the test macro).------Sanity Test on Oracle Upgrade DatabaseI do not think that you want to test Oracle 12c itself but if the applications still function. In that case I propose that the developers (or test team) perform there 'normal' application tests to see if the applications still function correct.The only thing that the DBA might give is information on the differences between Oracle10g and Oracle 12c at the handling of the data at SQL-level.------WMS WMTS TMS Server Stress ToolI also can recommend JMeter, as iant already mentioned. Its very flexible and after a while simple to use.If you look for something more "eye candy" like you can also try loadUI ( loadui.org/) which is a little bit more intuitive. Its not as flexible as Jmeter, but in my opinion its a more lightweight load testing tool which you can also use for monitoring purposes------5v Relay will not close (unless using GPIO cleanup)You can't use 5Â V relay with signal from Raspberry Pi while Raspberry Pi signal is 3.3Â V.So if you used Logic level converter to convert 3.3Â V from Raspberry to 5Â V then to relay in I think it may solve this issue. I don't know why most distributors say it should work with raspberry pi while the ideal one for Raspberry Pi is 3.3Â V relay. So you have 2 choices either: