Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

minimum of (n_{1}+n_{2}+n_{3})

If

Then Minimum value of

Where

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: minimum of (n_{1}+n_{2}+n_{3})

Hi juantheron;

You need more than that. The binomials are defined for negative integers and for rationals.

With the constraint that n1,n2,n3 ∈ N, I get,

With a minimum of 55.

With the way the problem is worded you have to solve a tough diophantine equation. A CAS is required. You need to provide a relationship between n1,n2 and n3. Is there one?

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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.

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: minimum of (n_{1}+n_{2}+n_{3})

Thanks bobym.. I dont have a knowledge od Diophantine equation..

So would you like to give me a document of Diophantine equation..

thanks.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: minimum of (n_{1}+n_{2}+n_{3})

Hi juantheron;

This is the equation that has to be solved.

So would you like to give me a document of Diophantine equation..

I wished I could. Everything I know about them was put together over many years. I do not know of a single good book on them although I have seen many. They are part of the field called number theory. I suppose the best books I have seen were "Recreations In The Theory Of Numbers" by Albert Beiler and the books of Waclaw Sierpinski. Hunt for them on the net and you will find them. They will provide you with the background you need and a smattering of diophantine equations.

---

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.