Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

3 diophantine equations

Hi;

Does anyone know of a proof that:

a + b = c

d + e = f

g + h = i

where a,b,c,d,e,f,g,h,i are different integers and  0 < a,b,c,d,e,f,g,h,i < 10, has no solutions.  I tried all nine numbers by computer and found no solutions. I haven't been able to prove it though.

---

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.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: 3 diophantine equations

The integers between 1 and 9 add to 45.
However, the total of the LHS's must be equal to the total of the RHS's, and so each of those would have to be 22.5. Hence, no solution.

---

Why did the vector cross the road?
It wanted to be normal.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 3 diophantine equations

Hi mathsyperson;

Want you to know I missed that idea completely. Thanks.

---

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.