Fermat's Little Theorem examples

[@chainag1829]

You are a fantastic teacher! Thanks so much.

[@MathsWithJay]

Thank you very much for your fabulous feedback.

[@theforceisnotwithyou]

This was honestly so helpful. I could not for the life of me understand how modulo notation worked, and seeing this explained with the theorem got me unstuck in the middle of a project. Thank you so much!

[@MathsWithJay]

Excellent! Thank you for letting us know - it is much appreciated.

[@ozzyfromspace]

Sometimes it’s better to see an application first, and only thereafter lean into the theory. Thanks, Jay, for starting me on the path towards understanding this beautiful theorem. Your examples were incredibly poignant 🏆🙌🏽🎊

[@MathsWithJay]

Glad to help! And thanks a lot for your fantastic feedback

[@tj9382]

The way you explain is nothing short of brilliant.

[@MathsWithJay]

Wow! Thank you T J

[@kamikiru1207]

Thank you so much! I have an exam tomorrow and homework due the next day and you just saved me! You explained so good! I worked your examples along with you...

[@MathsWithJay]

Brilliant! Good Luck for your exam, Carlos

[@wobblyjelly345]

Again, Maths with Jay saves the day. You are such a huge help, thank you 😊

[@MathsWithJay]

You are so welcome!

[@yanna6815]

I am a French student and this was the most helpful video I found, your explanation was clear and simple, I finally understood. Thank you !

[@MathsWithJay]

@Yanna Laurent: Thank you so much...merci beaucoup!

[@cary_domiii]

I've been struggling with this topic for days now in preparing to lecture this topic.... you've made it so easy to understand. Keep up the good work!

[@MathsWithJay]

Glad it was helpful!

[@AllenShen109]

You have saved my life! I needed to know how to do this for my Mathcounts, and I didn't know! Thank you so much!

[@MathsWithJay]

Wow...great to know we're saving lives!

[@AllenShen109]

:D

[@pixellatedpixie215]

You have saved me so much time and effort preparing for a test; thank you so much!

[@MathsWithJay]

You are so welcome!

[@rishisharma5249]

I love your Voice and really you are fantastic teacher I had ever met in my life Thanks for the video

[@MathsWithJay]

@Rishi: Thank you!

[@dimisword968]

Thank you so much, I am a native spanish speaker so I had been looking for spanish videos to figure that out and none of those videos worked for me and I found your video and it really helped me out!! . Finally I just got it

[@MathsWithJay]

Glad I could help! ¡Estoy aprendiendo español!

[@MathsWithJay]

Now with SUBTITLES

[@WelshGuitarDude]

Have i understood correctly here: 7^50 (mod 13) Since 7^12 = 1 mod 13 50 = 4 * 12 + 2 So 7^50 = 7^(4*12+2) = 1^4 * 7^2 = 1 * 49 = 10 mod 13 So least residue is 10 ?

[@BaneOfDarkness08]

THANK YOU THANK YOU THANK YOU! I'm in my final year as an undergrad in Computer Science and have been struggling dreadfully with congruences and residues. YOU ARE A LIFESAVER!

[@MathsWithJay]

N3rdRag3: Thank you! Good luck with the rest of your studies

[@kunalsinghgusain2070]

Loved it. Now I know the application of this theorem.

[@MathsWithJay]

@Kunal Singh Gusain: Excellent!

[@Vishnu-zk2nm]

Thanks Jay one of the best explanation I was in youtube you made it look very easy thanks...

[@MathsWithJay]

Great to hear!

[@saolaobri888]

This was extremely helpful having three levels of examples!

[@MathsWithJay]

Great to know!

[@atleastfortomorrow]

i ve seen 100 of videos and website this is by far the easiest solution

[@MathsWithJay]

@KAK: Thank you for your great feedback!!

[@HaGau-zk7rn]

Thanks for making this video. This is well explained. You are a great teacher!

[@MathsWithJay]

Thank you so much ♥️

[@altairezio6850]

Thank you very much for such a clear and an elegant explanation!

[@MathsWithJay]

@altair ezio: Thank you!

[@Robin-on6vo]

Thank you very much, helped me a lot for my first year of computer science study in france ! Best video on the subject on the 4 i watched

[@MathsWithJay]

Great to hear!

[@Sandra-nv9wm]

Thank you!! this really helped for my discrete mathematics class!

[@MathsWithJay]

That's great! Thank you so much for letting us know.

[@learnmathematics9382]

nice

[@igviness]

Mind blowing explanation. Really

[@MathsWithJay]

Thank you so much 😀

[@divyanshukumar8557]

i am from india jay, a student. We learn this type of things in senior High School (11th standard) but the methods are harder(Binomial theorem). This method is great.

[@MathsWithJay]

@Divyanshu: That's interesting. In England this sort of work is not done at school, only at university.

[@dylano5595]

Maths with Jay in countries such as India complex topics like number theory are introduced to students as early as secondary school. But these are just introducing the topic. When we get to college/uni that is when we learn it at the advanced level.

[@MathsWithJay]

@FAKEOUT DRAGON: Thank you for explaining that.

[@dharmendra8942]

can you tell that method to me?

[@bobboy6990]

Thanks a ton, my discrete math exam is in 2 hours and this was the last topic that was really giving me trouble and you cleared it right up

[@MathsWithJay]

@Bobboy6: Excellent - good luck with the exam!

[@pranavchaudhary2090]

Thanks!..It really helped me understand the theorem!!

[@MathsWithJay]

You are welcome!

[@psychalertgaming7675]

THANK YOU SO MUCH MAM... TOMORROW I'M HAVING MY MATHS EXAM.AND YOU REALLY HELPED ME

[@MathsWithJay]

Most welcome 😊 Good luck in your exam!

[@psychalertgaming7675]

Thank you mam

[@ikmal017]

Thank you, helped me a lot for Security System Theory exam

[@MathsWithJay]

Brilliant! It's great to know that this is still helping students.

[@chandlergersh]

Thank you! Your explanation was very clear and well paced

[@MathsWithJay]

Thank you so much - that is really useful to know.

[@samvoor496]

AWESOME!! very helpful. The Aussie accent made me feel much more sophisticated than i actually am hahaha!

[@MathsWithJay]

Great to hear!....Aussie?

[@OK-ri8eu]

This cleared a very annoying gap, thank you!!

[@MathsWithJay]

Glad it helped!

[@georgesos]

it took me quite a while to get it,then i came across this video!...the rest is history.:):)

[@MathsWithJay]

Brilliant! Thanks for letting us know.

[@glaxouszanofi4852]

Thank you so much you explained it better than my teacher

[@MathsWithJay]

Glad it helped!

[@DenysVitali]

Thank you for this lecture, it's fabulously explained, congrats!

[@MathsWithJay]

Thanks for this positive feedback.

[@snowboardparadise]

Hey there, nice video! Do you have a fast way to solve something like '2^550 (mod 551)', or is repeated squaring the only efficient way to solve that?

[@MathsWithJay]

Because 551 is not prime, you need to use Euler's Theorem here.

[@enzuber]

Thank you for a PERFECT explanation for my Year 7 class!

[@MathsWithJay]

@Nordin: It's great to know that this is useful. How old are your year 7's?

[@enzuber]

Maths with Jay 13 tears old. We do this topic in our enrichment work (early high school in Australia )

[@MathsWithJay]

@Nordin: Wow! That's impressive. I'm teaching this at a university. (By the way, in the UK, our year 7 students are 11 - 12 years old.)

[@factsverse9957]

Nordin Zuber I also need it for tomorrow for an Indonesian Olympiad for grade 9. And I'm also Grade 7.

[@vladyudashkin1471]

Coud you please explain why remainder does not stay the same for all primes? I tried your example with 2^50 breaking it down with all primes from 17 to 3. For all except 7 and 3 I got remainder 4, which means its composite. But for 7 and 3 I got remainder 1, which means its Prime. I will show it on paper: 2^50 = 2^(10*5) = 1 for P = 11 2^50 = 2^(2*25) = 1 for P = 3 Is there some kinda of rule for choosing primes you are checking for?

[@thezerothandtheinfinite]

I would guess it's because 50 = 5x5x2, 11-1=5x2; 3-1=2? Only just started this topic though so I don't know tbh

[@devanshparmar2845]

5 years later, still useful!

[@MathsWithJay]

Thank you...I guess mathematics doesn't change much over time

[@devanshparmar2845]

@@MathsWithJay NEVER CHANGES

[@dinhthaole3669]

This is great explanation. Thank you very much. Keep up the good work

[@MathsWithJay]

Thank you so much...it's great to see that a video from 2015 is still helping students!

[@cameronblack9174]

So helpful, thank you very much

[@MathsWithJay]

You're very welcome!

[@purodhachanuthika5898]

thankyou , i could not understand this leeson throughout my lectures in uni, then i looked into your video and i'm now so capable of doing this kinda sums.

[@MathsWithJay]

Excellent! Thank you!

[@sumanacharya3393]

I didn't understand the process of getting frome 16(mod 11) to direct 5(mod 11). Can you help me out here?

[@meeeeeepffxi]

Modular arithmetic is like a clock. Once you go around once, it resets back to 1. Alternatively, we can write 16=(11x1)+5=5mod11.

[@brendac271294]

Ugh math is amazing. Blows my mind every time I learn something new. Awesome video!

[@MathsWithJay]

Glad you liked it!

[@adrianharo6586]

Favorite video on Fermat's Little theorem, I like seeing examples.

[@MathsWithJay]

@Adrian Haro: Many thanks for this feedback

[@daneshsivakumar136]

Watching exactly one year after this was published xD. Great video, helped me with my Math Team HW. Thanks a ton! :D

[@MathsWithJay]

Thanks very much for your feedback

[@ball1stik766]

Great video. Cheers from the States! Thank you!

[@MathsWithJay]

@BaLL1sTiK: Thank you so much!

[@PoojaGusainMA-]

Thanks ❣ solving big examples is tricky but you made it so simple🙏🏻

[@MathsWithJay]

Most welcome 😊

[@millesaltskog]

Amazingly clear! Thank you! :)

[@MathsWithJay]

You're very welcome!

[@gaurav45098]

Thank you so much .you taught it so nicely .Thanks Thanks Thanks

[@MathsWithJay]

Thank you very much!

[@renan6827]

I was having trouble to understand it but you just made it easy.

[@MathsWithJay]

@Renan: Thank you!

[@lampochka3369]

It was very useful lesson, thanks.

[@love2aman]

Your are great mam..Such a beautiful explanation .. A big Thank You ! Much Love :)

[@Niteshmishraa]

I love your thick British accent! Much apreesh!

[@MathsWithJay]

@Nitesh Mishra: lol....thanks

[@che-maticschemistrymathema7044]

Thank you so much Ma'am for your nice explanation. It has helped me now. Thank you once again.

[@MathsWithJay]

@Ibaiahun Muthoh: Thank you so much!

[@che-maticschemistrymathema7044]

Welcome Ma'am and keep it up Ma'am 👍👍

[@quylongvo9041]

Grateful, i'm looking your video. Thanks so much

[@MathsWithJay]

You are welcome!

[@doctorscalling9479]

Thanks so much this made the subject more fun and easier

[@MathsWithJay]

I'm so glad!

[@denfarc]

Excellent explanation. Quickly understood. 👍👍

[@MathsWithJay]

Glad it was helpful! 😊😊

[@jagdeepshergill91]

Thank you. Really nice explanation!

[@MathsWithJay]

Thank you!

[@eslamasim8665]

Thanks for your effort, your explination is perfect

[@MathsWithJay]

Glad it was helpful!

[@rahmanmohamed9934]

Great work. Thanks

[@MathsWithJay]

@fahad: Thank you so much!

[@moayyadarz2965]

It a fantastic explanation Thank Jay

[@MathsWithJay]

Glad it helped!

[@nopecharon]

You are an awesome teacher : )

[@MathsWithJay]

Thank you! 😃

[@vf5400]

Thanks for sharing! Was very helpful

[@MathsWithJay]

Many thanks for your feedback. It is appreciated.

[@jaskaransingh6440]

thanku maths with jay... love u... plese also make a video on wavy curve(used for solving complex inequalities)

[@Welcome_cutie309]

Thank you... the explanation was superb.

[@MathsWithJay]

Thank you for this great feedback! I'm glad that you found this video useful.

[@dipeshrawat2587]

Thanks alot Jay, you saved me

[@MathsWithJay]

No problem 👍

[@hungryghost5589]

Really good video, thanks a bunch

[@MathsWithJay]

@nrmad: Thank you so much!

[@shoulderescape]

You are a lifesaver. Thank you!

[@MathsWithJay]

Glad to hear that!

[@zmrdotaurusrekt6901]

simple & perfect...thanks

[@MathsWithJay]

+ZmrDOTAurus Rekt Thank you so much for this positive feedback. Jay

[@R1C4RD0R3D15]

Great video, helped a lot. Keep up the great work

[@MathsWithJay]

+Jake Moore: Thanks for your feedback. Much appreciated. Jay

[@R1C4RD0R3D15]

Maths with Jay I've been looking around for something particular, maybe you know the answer. How can you do this exact thing but without prime numbers? For example, Find the remainder of 9^342 | 10

[@MathsWithJay]

+Jake Moore This is a different situation, so think about it in a different way: Start by writing down the first few powers of 9, find the remainders when you divide by 10, and you will see a simple pattern...

[@damonsweeney2124]

Great explanation, much appreciated.

[@MathsWithJay]

@Damon: Thank you!

[@pariminagalakshmi5517]

well, you r excellent!! super teaching!!...

[@MathsWithJay]

Thank you! 😃

[@christianjt7018]

Awesome explanation, thank you very much.

[@MathsWithJay]

Glad it was helpful!

[@spicyy812]

explained it so much better with examples than my book, tysm!

[@MathsWithJay]

You're very welcome!

[@DarkGT]

Realy helpful for my homework.

[@MathsWithJay]

Great!

[@cowgate]

You madam are a genius!

[@MathsWithJay]

Thank you!

[@shwetachoubey3944]

Very helpful we love your teaching 😍💝💝

[@MathsWithJay]

@shiveksha Choubey: Thank you so much...where are you?

[@shwetachoubey3944]

@@MathsWithJay I am here 😝

[@MathsWithJay]

:)

[@jashangill3237]

Thanks for explanation.😃

[@MathsWithJay]

:)

[@luisriba8082]

Do you divide 50 by 17 ? I think you get 50 = 17 * 2 + 16. Can you clarify please? Thanks

[@radhikaobhan7401]

the video is really helpful !! thanks a ton.

[@MathsWithJay]

Many thanks for your feedback.

[@PRAADHYUMNINDAANA]

Quick question, the formula said a^(p-1) is congruent to 1(mod p) right? So why in the problem of 2^50, did you do it to mod 17?

[@MathsWithJay]

p = 17 is prime

[@wtsfoodies]

In the 2nd example, you've taken p=50 and a=2. its not gonna prove fermat's little theorem because 2 is not relatively prime with 50. is'nt it wrong??

[@MathsWithJay]

p is 17 which is prime

[@jagdishsingh9266]

supeerb explaination..thnxx a lot

[@MathsWithJay]

Thank you so much for your positive feedback.

[@JohnSmith-bx4gf]

What if mod is larger than exponent?

[@MathsWithJay]

@John: How about trying this for small values and seeing what happens?

[@doyintalabi600]

thank you for simplifying this theorem

[@MathsWithJay]

You're very welcome!

[@ellasanchez4825]

Thank you so much for the clear explanation! Subscribed 😊

[@MathsWithJay]

Thanks for the sub!

[@2infinitybeyond655]

What if P is not prime?

[@MathsWithJay]

Good question...See kzbin.info/www/bejne/epjUlKWDgtaNgK8

[@navyakakarlapudi6126]

Good explanation mam.... Thank you so much....Mam.....

[@MathsWithJay]

Thank you!

[@xRASSAMx]

مادري كيف اوصف لك حبي ياعمري انتي والاكسنت حقتك

[@leelounsbury]

Great help! Thanks!

[@MathsWithJay]

That's good to know.

[@VatsalRajyaguru17143]

What if you used a number other than 2. You took the first number as 2^16. From that you could solve the second example 2^50 one. How would I solved let’s say 5^186 divided by 19??

[@MathsWithJay]

It's the number that you are dividing by that is important. 19 is prime, so 5^18 is congruent to 1....so write 186 as (19x?)+??

[@Junkycoders]

Thanks to u i finally understand it THX ❤❤

[@MathsWithJay]

@Hossam Ali: Thank you!!

[@s.y6371]

This is saving my life from discrete maths😭😭

[@MathsWithJay]

Excellent!

[@annaputland8831]

That was so easy to understand. Thank you

[@MathsWithJay]

Thank you!

[@ifechukwudenioweh6453]

WOW , your an amazing teachers, thanks a lot, you made it so easier.Your just the best

[@MathsWithJay]

Wow, thank you!

[@antuancaraballo9691]

Great examples, thank you!

[@MathsWithJay]

Thank you!

[@raheelbabz1378]

Very very helpful, thanks so much

[@MathsWithJay]

@Oxiide AspecT: Thank you very much!

[@3dy97]

Thank you, Teacher!

[@MathsWithJay]

You are welcome!

[@fanrco766]

Great video! Just wondering, why do you express the theorem as a^(p-1) = 1 mod p instead of as a^p - a = 0 mod p?

[@avni_isnt_smart]

It's the same thing!