euler's totient function: If gcd(a, n) = 1, then a^Phi (n) = 1 (mod n)

[Student x]

Hello,
I am trying to to proof that :

if gcd(a,n)=1 then a^Phi (n) = 1 (mod n)

Phi(n)= n-1

anyone can help please?

 

[Steven G]

Hello,
I am trying to to proof that :

if gcd(a,n)=1 then a^Phi (n) = 1 (mod n)

Phi(n)= n-1

anyone can help please?

Please tell us what you have tried and someone will guide you from there. Look at definitions!

 

[Student x]

Please tell us what you have tried and someone will guide you from there. Look at definitions!

I couldn't do it, so I don't know what you mean with tell you what I have tried, because if I tried and it was correct, I will not be asking that question.
And sometimes it is very helpful if people give the answer as a reply, by commenting on the message without any help, doesn't help , and just stops others from helping.
Thanks

 

[stapel]

I couldn't do it, so I don't know what you mean with tell you what I have tried, because if I tried and it was correct, I will not be asking that question.
And sometimes it is very helpful if people give the answer as a reply....

Actually, no; giving hand-in solutions has led in the past to driving out those students who'd wanted to learn, leaving us with only those who wanted to cheat. Sorry to be the bearer of that sad news.

You seem to feel that the only choices are (1) trying something and successfully reaching the desired final result or, on the other hand, (2) doing absolutely nothing at all. There is a third option, which was requested of you by the first helper: (3) trying something, but it doesn't end up where you want it, so you ask for advice.

Please do at least attempt this exercise, even if you don't think you can see your way to the end. Then, if you get stuck, you can reply with whatever you've tried so far, at which point we can "see" your reasoning, and reply with suggestions to get you going again.

Thank you!

 

[Student x]

Actually, no; giving hand-in solutions has led in the past to driving out those students who'd wanted to learn, leaving us with only those who wanted to cheat. Sorry to be the bearer of that sad news.

You seem to feel that the only choices are (1) trying something and successfully reaching the desired final result or, on the other hand, (2) doing absolutely nothing at all. There is a third option, which was requested of you by the first helper: (3) trying something, but it doesn't end up where you want it, so you ask for advice.

Please do at least attempt this exercise, even if you don't think you can see your way to the end. Then, if you get stuck, you can reply with whatever you've tried so far, at which point we can "see" your reasoning, and reply with suggestions to get you going again.

Thank you!

You sound like if you know me and like if you know what I tried and what I haven't, but I don't know why some people come to those websites and forums and try to be psychologist, I am here asking if anyone can help me to solve a problem, who are you to say I am cheating, it is maybe because when you were student you cheated that is why you think everyone is the same, or probably because the knowledge that you got make you believe you can have the arrogance to treat others that way. I don't know you personally, you might be a genius in maths, but one thing is sure: you are very rude. please just don't reply, and if anyone think the same as you, then no need to reply. there are people that want to help, the question posted was to them, and not to people that want to put student down. So if anyone want to help, I am very grateful , but if anyone is just giving blabla advise about the nonsense they believe then please just leave it .
thanks

 

[Deleted member 4993]

You sound like if you know me and like if you know what I tried and what I haven't, but I don't know why some people come to those websites and forums and try to be psychologist, I am here asking if anyone can help me to solve a problem, who are you to say I am cheating, it is maybe because when you were student you cheated that is why you think everyone is the same, or probably because the knowledge that you got make you believe you can have the arrogance to treat others that way. I don't know you personally, you might be a genius in maths, but one thing is sure: you are very rude. please just don't reply, and if anyone think the same as you, then no need to reply. there are people that want to help, the question posted was to them, and not to people that want to put student down. So if anyone want to help, I am very grateful , but if anyone is just giving blabla advise about the nonsense they believe then please just leave it .
thanks

That is exactly what we want to know! And we would know that if you share your work/thought with us.

We do not know whether you know the meaning of "Totient functions" or not!

Instead of being defensive about your deficiencies, help us to help you by letting us have a "feel" for where should we start this help.

Do we need to start with the definition of prime numbers?

 

[Student x]

That is exactly what we want to know! And we would know that if you share your work/thought with us.

We do not know whether you know the meaning of "Totient functions" or not!

Instead of being defensive about your deficiencies, help us to help you by letting us have a "feel" for where should we start this help.

Do we need to start with the definition of prime numbers?

I know the meaning of totient functions, and I don't need the definition of prime numbers,
As I said I tried to use the gcd properties to show that, I wasn't successful, and I tried using the properties of Totient function, and I wasn't successful, It is the Euler Totient theorem, and which is the origine of the Fermat little theorem, that I had to proof. the Fermat little theorem, I knew how to prove it, but this theorem is more general one, and I don't know how to do it, I will have to use the basic properties of those two things, I can't just say because it is totient function and we know it is true. I really don't know why is it hard for someone that knows the answer to simply share it without giving a lesson . I really spent too much time trying to do it, and I know it is not schience fiction, when I see the proof, I will understand it and will learn from it , that way I may be able to prove other things using similar technique, but at the moment, I don't really know how to do it. and I don't see it as deficiencies Mr/Ms Khan

 

[Deleted member 4993]

I know the meaning of totient functions, and I don't need the definition of prime numbers,
As I said I tried to use the gcd properties to show that, I wasn't successful, and I tried using the properties of Totient function, and I wasn't successful, It is the Euler Totient theorem, and which is the origine of the Fermat little theorem, that I had to proof. the Fermat little theorem, I knew how to prove it, but this theorem is more general one, and I don't know how to do it, I will have to use the basic properties of those two things, I can't just say because it is totient function and we know it is true. I really don't know why is it hard for someone that knows the answer to simply share it without giving a lesson . I really spent too much time trying to do it, and I know it is not schience fiction, when I see the proof, I will understand it and will learn from it , that way I may be able to prove other things using similar technique, but at the moment, I don't really know how to do it. and I don't see it as deficiencies Mr/Ms Khan

Did you read:

https://en.wikipedia.org/wiki/Proofs_of_Fermat's_little_theorem