Math Is Fun Forum

evene

Member

Registered: 2015-10-18

Posts: 272

Showing that two equations are actually equal

Is there a way to show that

is equal to

?

I've found that

and

Last edited by evene (2016-10-22 04:42:58)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Showing that two equations are actually equal

Hi;

Not to be funny but can you say something about "something".

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Showing that two equations are actually equal

Um... they are unknowns that need to be determined. I do know that they are in the form

for special integer k. Although I don't know what k is... That's what I'm trying to find.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Showing that two equations are actually equal

Hi;

A computer search for integers -40 <= a,b,c, <=60 did not find any answers of the form

I can widen the search using a pslq but I think you want small constants as your examples suggest.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Showing that two equations are actually equal

Yes. I have figured it out. We have

Turns out, there are 5 of the cos(x) thing...

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Showing that two equations are actually equal

That is why I did not find any. I thought you wanted 3.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Showing that two equations are actually equal

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Showing that two equations are actually equal

Hi;

It turns out, that the number of cosines are m where 6m+1=p where p is the roof of unity.

How do you know that is true?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Showing that two equations are actually equal

Lots of internet searching...

Focusing on Ramanujan's method for solving these types of equations might also be a big factor.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Showing that two equations are actually equal

Hi;

Ramanujan's method? Got a link?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Showing that two equations are actually equal

Actually, this isn't Ramanujan's method. But doing an extensive amount of internet searching, you can find theorems such as these.