sum of two squares????

[smslca]

If an Even number could be expressed in the form a² + b² . And if there exits two other numbers m,n such that
a² + b² = m² + n²

then , my question is

is there any relation between (a,b) and (m,n) apart from a² + b² = m² + n² ??

 

[jeevan.life]

can you prove that the above equation holds good for any set of numbers...

 

[smslca]

can you prove that the above equation holds good for any set of numbers...

I did not say for any given (a,b) there surely exits (m,n)

I said " If " p is even and " if " p = a^2 + b^2 = m^2 + n^2 , then what is the relation between a,b,m,n other than p = a^2 + b^2 = m^2 + n^2 equation.

 

[andre_luis]

smslca,

Yes...There are a trigonometric relationship :

**broken link removed**

You can convert that variables to polar coordinates.

+++

 

[smslca]

smslca,

Yes...There are a trigonometric relationship :

You can convert that variables to polar coordinates.

+++

That's somewhat new and interesting to me

 

[zorro]

The question has sense only if you specify that a, b, m, and n are all integers. Otherwise, the problem is trivial; there is an infinity of solutions for every even p.
Regards

Z