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#51 Re: Help Me ! » Ramanujan and his e power equation » 2016-11-06 11:52:31
Yes.
What is a Klein Absolute Invariate?
What is an algebraic integer?
What is a class number?
And what is the prerequisite knowledge to this.
#52 Re: Help Me ! » What condition makes this equation true? » 2016-11-05 11:57:53
No, you don't have to explicitly solve for m. I just added that, because I thought that solving for m would help find the actual constraint.
#53 Re: Help Me ! » What condition makes this equation true? » 2016-11-05 09:35:16
Like, you can't simply say
"The equation is satisfied when
"Because.... well... that's obvious... right?
I'm just looking for simpler cases when both sides are equal.
#54 Re: Help Me ! » Ramanujan and his e power equation » 2016-11-05 09:32:05
Now, let d be a positive square free integer in . And let
Thus
Respectively. Therefore, j(q) is an algebraic integer of degree h(d) where h(d) is the class number of Q(i*√d).
I need help breaking down this theorem.
#55 Re: Help Me ! » What condition makes this equation true? » 2016-11-05 09:25:48
Yes, m,n,s,t ≠ 0. And you cannot just restate the problem.
#56 Re: Help Me ! » Solving for m in terms of n,s,t » 2016-11-05 06:14:36
Thanks! That helped a lot.
How did you see that?
#57 Help Me ! » What condition makes this equation true? » 2016-11-05 06:08:20
- evene
- Replies: 13
I have the following equation
And I need a condition for them to be equal. So my problem is: What is that condition?
Please no trivial answers please.
#58 Help Me ! » Solving for m in terms of n,s,t » 2016-11-04 12:19:59
- evene
- Replies: 2
In need help with solving
for m in terms of n,s,t.
How do I evaluate this? (Note that I mostly need help with the actual algebra part)
#59 Re: Help Me ! » Ramanujan and his e power equation » 2016-11-03 14:41:49
And unfortunately, it only works with Heegner numbers.
Implying one cannot evaluate
At all...
#60 Re: Help Me ! » Help! » 2016-11-03 14:40:37
Complicated logic? I don't understand.
#61 Re: Help Me ! » Help! » 2016-11-03 10:38:54
Another way, is to notice that the coefficients go in a,b,a.
Dividing both sides by x, we arrive at
And isolating x, we get
And by Vieta's formula, we see that the other root must be 1/4.
#62 Re: Help Me ! » Ramanujan and his e power equation » 2016-11-03 09:36:14
Wait, what do you mean by "what happens next"?
I'm just as stumped. I don't know why the formula works and how it works. I just know that it works.
#64 Re: Help Me ! » Functions » 2016-11-03 05:32:06
Um... compound interest vs. simple interest..?
#65 Re: Help Me ! » Ramanujan and his e power equation » 2016-11-03 05:30:04
Actually, I now think the problem is a bit "redundant"..?
Wikipedia describes a simple procedure. And I know what to do, but I don't understand why that method works and why they got the steps. Unfortunately, it only works on Heegner numbers. (Implying that you can't evaluate with it)The concept is simple.
For d is a Heegner number (19, 43, 67, 163) You can find the approximation using the q-expansion (). But I don't know how to evaluate it.
#66 Re: Help Me ! » Ramanujan and his e power equation » 2016-11-02 10:12:42
@bobbym What's plsq?
@zetafunc I understand the part where you said Taylor series expansion, brilliant that is! But how would you calculate the infinite sums?
Given
We have
How would you calculate the infinite sum? I haven't learned taylor expansion yet, so sorry if that question seems a bit stupid.
#67 Re: Help Me ! » Solving for the unknowns in a diophantine equation » 2016-11-02 10:08:59
Sure.. determinant...
Why is division by a matrix not defined? Isn't a matrix simply subtracting values, given the fact that the elements of the matrix can never all equal 0...
#68 Help Me ! » Ramanujan and his e power equation » 2016-11-02 09:43:22
- evene
- Replies: 19
Note that Ramanujan found this a long time before computers. Thus, he had to have a method for calculating these transcendental numbers!
#69 Re: Help Me ! » Showing that two equations are actually equal » 2016-11-02 09:40:45
Actually, this isn't Ramanujan's method. But doing an extensive amount of internet searching, you can find theorems such as these.
#71 Help Me ! » Solving for the unknowns in a diophantine equation » 2016-11-02 07:40:29
- evene
- Replies: 5
I didn't really try much due to the sheer ugliness of the system and how intimidating it looks. I want the to be in "matrix" form. Meaning if $\alpha$ is expressible as , instead, write . I have provided an example below:
Example: Find from the following:
I have found the solutions as
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#72 Re: Help Me ! » Showing that two equations are actually equal » 2016-11-02 06:03:52
Lots of internet searching...
Focusing on Ramanujan's method for solving these types of equations might also be a big factor.
#73 Re: Help Me ! » Showing that two equations are actually equal » 2016-10-31 14:40:48
Yes. I realized that.
It turns out, that the number of cosines are m where 6m+1=p where p is the roof of unity. So for my example, the pth root of unity was 31. Thus, m=5 and we have
#74 Re: Help Me ! » Showing that two equations are actually equal » 2016-10-31 11:22:49
Yes. I have figured it out. We have
Turns out, there are 5 of the cos(x) thing...
#75 This is Cool » New radical formula? » 2016-10-31 11:17:43
- evene
- Replies: 3
See if you can algebraically prove
Bonus points if you can prove it without the use of a computer or wolfram alpha!
