# Math Help - Making numbers add up to square numbers

1. ## Making numbers add up to square numbers

Hi everyone,

I'm stuck on this question and it's driving me crazy!!

Basically you have to add numbers in a line of a triangle that will add up to a square number.

e.g. a
b c

a&b have to add up to a square, as well as a&c and b&c.

Any help would be appreciated.

Can anyone help?

2. Originally Posted by Markdevs
Hi everyone,

I'm stuck on this question and it's driving me crazy!!

Basically you have to add numbers in a triangle that will add up to a square number.

Can anyone help?
you may want to be a little more specific than that

3. Originally Posted by Markdevs
Hi everyone,

I'm stuck on this question and it's driving me crazy!!

Basically you have to add numbers in a line of a triangle that will add up to a square number.

e.g. a
b c

a&b have to add up to a square, as well as a&c and b&c.

Any help would be appreciated.

Can anyone help?
Do you mean like
Code:
  -1
2    2
Or is there some restriction on the numbers a, b, c?

-Dan

4. Originally Posted by Markdevs
Hi everyone,

I'm stuck on this question and it's driving me crazy!!

Basically you have to add numbers in a line of a triangle that will add up to a square number.

e.g. a
b c

a&b have to add up to a square, as well as a&c and b&c.

Any help would be appreciated.

Can anyone help?
Code:
   a
b    c
such that
$a + b = x^2$

$a + c = y^2$

$b + c = z^2$

Subtracting the first two equations gives me
$a - c = x^2 - y^2$

Adding this equation to the third equation give me
$2b = x^2 - y^2 + z^2$

Thus
$b = \frac{x^2 - y^2 + z^2}{2}$

$c = z^2 - \frac{x^2 - y^2 + z^2}{2} = \frac{-x^2 + y^2 + z^2}{2}$

$a = x^2 - \frac{x^2 - y^2 + z^2}{2} = \frac{x^2 + y^2 - z^2}{2}$

You can pick any numbers x, y, z that you like.

For example, letting x = 1, y = 2, and z = 3 gives
Code:
   -2
3    6
-Dan

EDIT: I can show that at least one of a, b, and c must be negative.