Euler totient function made easy

[@timothywahib6082]

You are literally the best human on this planet

[@RandellHeyman]

Thanks Timothy, hope your mathematics is going well.

[@timothywahib6082]

@@RandellHeyman it is thanks to you, I had no idea what I was doing before

[@HansFlamme]

Impeccable explanation I finally get it, thank you very much sir

[@RandellHeyman]

Thanks for taking the time to comment.

[@sleeplesshead602]

I'm just a random youtube viewer that is to curious about Euler's Phi. I only got the solution for prime number. Thanks for the explanation. Now I got it.

[@RandellHeyman]

I'm glad I could help you.

[@badradish2116]

thank you for saving me from my useless number theory book.

[@RandellHeyman]

Glad it helped. More time saving videos at kzbin.info

[@yasmin9718]

@@ParamjitSingh-gz3de ok

[@monicabrasow5402]

You have a very clean mind! Genius!

[@RandellHeyman]

Thanks for such positive comments. I'm glad it helped.

[@SaiBharatBatchu]

wtfffff only 299 views for such a master piece ?? :(

[@gorymclorry7414]

3,200 now.

[@electrotsmishar]

same question

[@parasgathani4784]

20k now

[@Man-ds9ir]

33k now

[@kumarshanu4524]

44k now

[@conradt.s]

Finally got the sense of Euler's function here..... Good explanation Sir...

[@RandellHeyman]

Thanks. You might be interested in the related videos, Euler's theorem made easy, Fermat's little theorem made easy and if you study encryption then RSA code made easy.

[@kid5hinobi848]

Thank you a bunch. Been trying to solve Liber Primus and I think this will definitely help.

[@aishwaryaratnam154]

Hey bro this was exactly a masterpiece.hats off to you.

[@RandellHeyman]

Thanks very much.

[@urajunky]

This guy is the man!!! please take over Deakin Uni maths!

[@RandellHeyman]

Thanks for such positive comments.

[@kneebrain9298]

ahhh i got finals tomorrow and this helps me a lot!! thank you so much 💝💝

[@RandellHeyman]

Thanks. Hope the finals go well.

[@Imperator-SPQR]

You deserve more views. Thanks for posting

[@RandellHeyman]

Thanks Jun, I have other related videos that might be useful: Euler theorem made easy, Fermat's little theorem made easy, etc.

[@_koppy1309]

I remember trying to use the 4th rule and hating it. Loved the simplicity of the first three rules. Just found your videos and wish I had watched them in when I was in college!

[@RandellHeyman]

Thanks for letting me know that you found the video helpful.

[@ListRav17]

Very well made! Many videos I watch simply mention the end algorithm, but I enjoy using the rules.

[@RandellHeyman]

Great. It's better to know the rules for doing more/harder mathematics.

[@leviticus3]

Well explained! Thank you for this.

[@j.vonhogen9650]

Excellent explanation! Thank you so much!

[@RandellHeyman]

Thanks for taking the time to comment. I have related videos that also might be useful: Euler's theorem made easy, Fermat's little theorem made easy and if you study encryption then How encryption works and RSA code made easy.

[@j.vonhogen9650]

@@RandellHeyman - Thanks, I was already 'binge watching' your videos! Great content, wonderfully explained, greatly appreciated! 😎👍 Greetings from The Netherlands!

[@ropafadzomaseko7135]

super easy to understand ,,,l loved it explained better than my lecturere would have :-)

[@RandellHeyman]

Thanks. I also have videos on related topics if/when you need them: euler's theorem made easy and fermat's little theorem made easy.

[@patrick-cc4yu]

Finally! The 27.8k views you deserve!!!

[@RandellHeyman]

Pat, I'm glad it helped you. I have some other related videos if you are interested...euler's theorem made easy, fermat's little theorem made easy, how encryption works, RSA code made easy.

[@foobar4938]

@@RandellHeyman Hey man, i never comment. But i had to tell you how thankfull i am for this.

[@RajdeepBarman]

I found a gem of a tutorial

[@RandellHeyman]

Thanks for the comment.

[@xbz24]

Thanks a bunch❤

[@kibaekim501]

Rule 2 is a generalization of Rule 1. phi(p^1) = p^1 - p^(1-1) = p - 1

[@RandellHeyman]

Exactly right. From a teaching view I think it best to have separate rules. Thanks for commenting.

[@leaha2357]

Brilliant explanation, so clear :)

[@RandellHeyman]

Thanks. I have some related videos, e.g. Euler's theorem made easy, Fermat's little theorem made easy, RSA code made easy.

[@divinetakawira5420]

What a masterclass.

[@RandellHeyman]

Thanks for the positive feedback.

[@DaveandEm2000]

Thanks for making this video. It helped me out alot.

[@RandellHeyman]

Glad it helped.

[@samueldeandrade8535]

0:04 no, that's the null sign, the symbol to denote the empty set. Phi is something else.

[@RandellHeyman]

You are correct. I think at the time I just used what was in Word. But that's no excuse. Thx for pointing it out.

[@samueldeandrade8535]

@@RandellHeyman hehe. That's nice. I really don't care about the notation, you did a good job. Keep doing it. We need good math content creators.

[@moppop275]

Thank you for the video, i found it useful!

[@RandellHeyman]

Thanks for letting me know :)

[@דניאל-ט9ד]

great video. thank you!

[@RandellHeyman]

I'm glad it helped you.

[@Mordicsilva]

Thank you sir🙏

[@pradyundevarakonda6849]

Thank you sir, you really made it easy.

[@RandellHeyman]

Thanks. I have related videos on Euler's theorem, Fermat's little theorem, how encryption works and RSA code if you need them.

[@JannisAdmek]

thank you soo much, guys like you make my life easy :D

[@RandellHeyman]

Thanks. I have a few related videos: fermat's little theorem made easy and eulers theorem made easy. For use in cryptography there is RSA code made easy.

[@JannisAdmek]

Randell Heyman I am on a marathon through your channel, amazing

[@regenciaamiragracer.4524]

Thank you very much.

[@RandellHeyman]

Thanks. Lots of related videos on my channel

[@PETAJOULE543]

Great explanation about euler totient function that is simply amount of gcds' that gcd=1.

[@RandellHeyman]

Thanks

[@clive_clive]

great video

[@RandellHeyman]

Thanks for the positive feedback. I have a few related videos: Euler's theorem made easy, Fermat's little theorem made easy.

[@Abdulaziz-fg3mh]

THANK YOU!

[@sonic10ultimate]

Amazing, thanks

[@RandellHeyman]

Thanks for your comment. I have related videos on Euler's theorem, Fermat's little theorem, How encryption works and RSA code that might also be useful to you at some stage.

[@sonic10ultimate]

@@RandellHeyman Thank you, I'll probably end up watching ones related to RSA

[@renumehra4619]

amazing…Thank you!

[@RandellHeyman]

Thanks. Many relayted videos in my University mathematics and Coron help playlists.

[@abdibaqihassanomar5900]

Thanks Mr it helped me a lot to understand phi functions but still i confuse Fermat's Theorem and Euler's Theorem

[@RandellHeyman]

Have a look at my videos Euler's theorem made easy and Fermat's little theorem made easy.

[@gigispace]

thank you!

[@RandellHeyman]

As we say in Australia...no worries. Thanks.

[@shakeeljessa9619]

Very helpful, thank you!

[@RandellHeyman]

Shakeel Jessa Glad it helped.

[@arizonajterm3984]

Thanks. This is a great video, but is there a function that takes into account all the things you take for granted in these rules? For example, you for 600, what's the function you used to figure out that you could use 2^3 * 3 * 5^2... Also, 41 is easy to identify as a prime, but what about large numbers that you may not be sure if they are prime... just curious about your thoughts on that. Thanks.

[@RandellHeyman]

Arizona Jterm There are algorithms for factoring large numbers into its divisors and for determining if a number is prime. Factoring large numbers is a slow process for very large numbers. Amazingly this slowness has been turned into an adantage (in cryptography) using the euler totient function. See my videos 'how encryption works' and then my other video 'RSA code made easy'.

[@debjitkhaskel7879]

Really Liked It and helpful :)

[@debjitkhaskel7879]

correct

[@RandellHeyman]

Thanks. I recently uploaded related videos Euler's theorem made easy and Fermat's little theorem made easy.

[@giovannimoncada1945]

thank you ❤

[@RandellHeyman]

Giovanni, I'm glad it helped you. Related videos on my channel...euler's theorem made easy, fermat's little theorem made easy, how encryption works, RSA code made easy.

[@sumitjha392]

Thank you sir, that helped :)

[@RandellHeyman]

Sumit Jha Glad it helped. I'll probably have a video on euler's theorem (which uses the euler totient function) soon.

[@electrotsmishar]

awesome

[@RandellHeyman]

Thanks for letting me know.

[@stevenwilson5556]

for phi(p^n) = p^n - p^(n-1), doesn't that equal (p^n)*[ (p-1)/(p)] ? Example phi(2^3) = 2^3 - 2^2 = 8-4 or (8 * (2-1)/2). And phi(3^2) = 9 - 3 = 9*[ (3-1)/3 ], phi(5^3) = 125 - 25 = 125 * [(5-1)/5]… am I wrong or doesn't this pattern hold in general?

[@RandellHeyman]

You are correct. Also p^n-p^(n-1)=p^(n-1)[p-1].

[@khadijakhan7770]

nice

[@RandellHeyman]

Thanks. I have 2 related videos: Euler's theorem made easy and Fermat's little theorem made easy.

[@Akkryon]

3301

[@ivandrofly]

3:43

[@alainrogez8485]

I am confused because you prove nothing.

[@RandellHeyman]

This was to help people with the standard test / exam questions like calculate phi(100). If you are having trouble proving something let me know.