1. Jan 28, 2013

### cragar

1. The problem statement, all variables and given/known data
Prove that 2n is representable when n is. Is the converse true?
Representable is when a positive integer can be written
as the sum of 2 integral squares.
3. The attempt at a solution
so n can be written as $x^2+y^2$
x and y are positive integers
so then $2n=2(x^2+y^2)$
Im not really sure where to go next, maybe i should look a the prime factors.
Just to make sure that i know what converse is,
Would the converse be if 2n is representable so is n.

2. Jan 28, 2013

### Dick

Brahmagupta–Fibonacci identity. Look it up. And yes, that would be the statement of the converse.

3. Jan 29, 2013

### SammyS

Staff Emeritus
Try some specific examples, like 25 = 32 + 42

or 29 = 22 + 52 .

Yes, that's the converse.

4. Jan 29, 2013

### cragar

ok thanks for the responses. Knowing my teacher I would need to prove the
Brahmagupta–Fibonacci identity, but I guess I could multiply it out and show that
the left side equaled the right side. I think the converse is true but ill think about how to prove it.

5. Jan 29, 2013

### Dick

Yes, you should definitely think much harder about the converse. And sure, it's much easier to prove them than to discover they exist.

Last edited: Jan 29, 2013