Math Is Fun Forum

FERMAT'S

Member

Registered: 2011-01-17

Posts: 29

who can solve it ??

:

if x,y,z are Integers numbers but not negative (0,1,2,3,4,5,6...........))
(( if u have other sentence better than this please tell me ))

how many solutions there are in this formulas.

x+y+z=2

and what are they ??

I know it is easy question , I just wanna be sure of something

thanx :):):)

Last edited by FERMAT'S (2011-01-18 18:47:45)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: who can solve it ??

Hi;

There are no solutions.

---

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.

FERMAT'S

Member

Registered: 2011-01-17

Posts: 29

Re: who can solve it ??

Sorry there was a mistake in the quastion

I fixed the mistake

thank u

Last edited by FERMAT'S (2011-01-18 18:38:18)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: who can solve it ??

Hi;

There are 6 solutions now.

---

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.

FERMAT'S

Member

Registered: 2011-01-17

Posts: 29

Re: who can solve it ??

ok thanx for that

what about if we say  a+b+c+d=8

how many solutins there are ?

FERMAT'S

Member

Registered: 2011-01-17

Posts: 29

Re: who can solve it ??

actually I read  a rule says

if x1,x2,x3,........,xn Integers numbers but not negative
so the number of solutions for x1+x2+x3+x4+........+xn=j

is
(n-1+j)C j 

I Wanna be sure if is it right ?

Last edited by FERMAT'S (2011-01-18 19:00:03)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: who can solve it ??

That is correct.

That is for x + y + z = 2

Use the same formula for a+b+c+d = 8

---

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.

FERMAT'S

Member

Registered: 2011-01-17

Posts: 29

Re: who can solve it ??

thank u so much

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: who can solve it ??

Hi;

This is how a+b+c+d = 8 is solved using an ordinary generating function.

See the coefficient of the x^8 term, that is the answer.

---

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.

FERMAT'S

Member

Registered: 2011-01-17

Posts: 29

Re: who can solve it ??

woOoOow

I will think about it , thank u for the hint for a new problem
I tried to prove this rule >>> (n-1+j)C j , I wondered from where the Combinations came ?

I have quastion is there a link for IMO training in this forum.:

Last edited by FERMAT'S (2011-01-18 19:31:16)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: who can solve it ??

Hi;

I wondered from where the Combinations came ?

Do you remember ever having done a spaces and o problem? That is a bijection with the number of solutions of a linear diophantine equation. That is where the combinations come from.

No link that I know of but just post your questions.

---

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.