first power plus dNUMBER_TOKEN times NUMBER_TOKEN to the zero power now how does this help well the cool thing is now and by coincidence the one plus d naught is going to end us up with another digit yet again this digit being the number four right here okay and you can see the correspondence here dNUMBER_TOKEN is still our three which fits this definition and also the not is going to be one which is the in in the hundredth place this is good if it's not the case and and you're going to trigger one over to the next um digit blaze you have to use modular arithmetic but in this easy example it's it's very easy to see how everything works now cool thing is alternating digit sum just tells us something about how we are going to treat our hundredth tenth and one place and so on thousands place etc namely what we're going to do is we're going to start with in our case the NUMBER_TOKENth place digit okay alternating digit sum NUMBER_TOKEN place digit then we are going to subtract our digit from the NUMBER_TOKENth place from it so negative dNUMBER_TOKEN plus d naught and we are going to add our digit from the um one place to it plus tNUMBER_TOKEN by using the distributed flows here we are going to get that this is d naught minus dNUMBER_TOKEN and then distributing negative signs here too negative d naught plus t one and now you can see the magic happen d naught is going to cancel out dNUMBER_TOKEN is going to cancel out giving us zero overall as the alternating digit sum we basically turn this process with numerics okay just this easy number example into something more abstract and then the alternating digit sum basically popped out giving us zero telling us overall that NUMBER_TOKEN must be a number divisible by NUMBER_TOKEN. i mean this right here is basically just an equivalent way of rewriting it meaning this right here proves for num level number NUMBER_TOKEN that is going to be a number divisible by NUMBER_TOKEN. but for more complex numbers okay not complex numbers in the sense of complex numbers but for numbers whether where one is going to be tracked over to another tenth place it becomes a bit more delicate and you have to deal with modular arithmetic as mentioned before but overall the process stays the same and this is how you can check if a number is divisible by NUMBER_TOKEN or not so here for the people who always wondered how to divide numbers by NUMBER_TOKEN here's the trick and i hope you did enjoy what you have seen today and if you want to see more number theory algebra and all the other things that we did today divisibility rules competitive mathematics then i invite you to check out the consoles of today's sponsored brilliant we're kind enough to sponsor yet another video here on this channel as mentioned just a second ago over on brilliant you can find a lot of topics in mathematics number theory algebra also abstract algebra competitive mathematics and many more and it doesn't stop there brand is your source for some of the best interactive online learning content out there on the internet and they specialize on stem content stem education be it chemistry physics mathematics philosophy search engines they also got that whatever it is you are seeking for prayer definitely has something up the sleeve for you and their interactive content is something that's very dear to my heart i use brilliant on a weekly basis basically on a regular basis and i even show even though the website is in english
START_SPONSOR_TOKEN check out the consoles of today's sponsored brilliant we're kind enough to sponsor yet another video here on this channel as mentioned just a second ago over on brilliant you can find a lot of topics in mathematics number theory algebra also abstract algebra competitive mathematics and many more and it doesn't stop there brand is your source for some of the best interactive online learning content out there on the internet and they specialize on stem content stem education be it chemistry physics mathematics philosophy search engines they also got that whatever it is you are seeking for prayer definitely has something up the sleeve for you and their interactive content is something that's very dear to my heart i use brilliant on a weekly basis basically on a regular basis and i even show even though the website is in english END_SPONSOR_TOKEN