On 19/05/2013 13:15, Jasen Betts wrote:
On 2013-05-19, Martin Brown wrote:
On 18/05/2013 23:10, Tom Del Rosso wrote:
Martin Brown wrote:

given a^2 + b^2 = c^2 where a,b,c are integers

can you construct A^2 + B^2 = 2c^2 and state A, B

A=B=0

But I get the impression that's not what you had in mind?

I forgot to exclude a=b=0 in the problem statement
although we normally allowed that option as a first try

But there is another solution with a, b, A, B != 0

probably you should have said positive integers at the start.

I should perhaps have said non-zero but it was normal not to bother.

The even powers mean that positive or negative makes no difference.

Anyone that didn't spot a=b=A=B=0 as a solution would fail immediately.

anyway:

a,b,A,B

5,5 (and more variations on Pythogaras triangle hypotenuse)

1,7 and probably more like that too, certainly multiples of it.

Valid concrete examples I grant you.

The final problem statement is for given a,b,c with

a^2 + b^2 = c^2

find algebraic expressions for A,B

s.t A^2 + B^2 = 2c^2

--
Regards,
Martin Brown