Equation rule

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SherlockWante

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(a - b) * c = k * 21 Since gcd (c, 21) = 1, every prime factor of c must be contained in k, i.e. k = lc for certain whole l, so (a-b) c = l * c * 29.
Can someone explain me why every prime factor of c must be contained in k? Thank you in advance.
 
Suppose that there was some prime factor d of c that did not divide k. That is, c = hd. Can you find a contradiction?

Or, you can just think informally: If we factor each side completely, each prime factor of c must be somewhere on the right side. Where can it be?

I still don't think you have told us what you have learned about number theory, on which we can base an explanation. Please do so. All we know is that you have learned something about modular arithmetic, but not much.
 
Dr.Peterson said:
Suppose that there was some prime factor d of c that did not divide k. That is, c = hd. Can you find a contradiction?

Or, you can just think informally: If we factor each side completely, each prime factor of c must be somewhere on the right side. Where can it be?

I still don't think you have told us what you have learned about number theory, on which we can base an explanation. Please do so. All we know is that you have learned something about modular arithmetic, but not much.
Click to expand...
Thank you very much! I have actually learned nothing about number theory. I am just searching for myself and trying to solve some exercises.
I have basic math knowledge, but not about number theory.
 
Dr.Peterson said:
Suppose that there was some prime factor d of c that did not divide k. That is, c = hd. Can you find a contradiction?

Or, you can just think informally: If we factor each side completely, each prime factor of c must be somewhere on the right side. Where can it be?

I still don't think you have told us what you have learned about number theory, on which we can base an explanation. Please do so. All we know is that you have learned something about modular arithmetic, but not much.
Click to expand...
But why is k=l*c and not k=d*h because c=d*h?
 
SherlockWante said:
But why is k=l*c and not k=d*h because c=d*h?
Click to expand...

Well, you can't say k = dh, because that would mean k = c, which is not necessary.

What did you do with my suggestions? Please show me your thinking.

But I think you really need to work through some material on number theory, rather than just read random material that you are not ready for. I searched for free introductory material, and found these that you might look at, to see if they communicate clearly to you:

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By reading through a text of some sort, you can expect to know the required facts before you are asked to use them, which is much more efficient than random learning.
 
Thank you very much for everything! I will read them and then I will try the x^5 one.
But can you check in my other post if I'm right by saying x^5≡ y^5 <=> x≡ y
After I have solved this last problem, I will directly start reading some introductory material.
 
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