Ramanujan's magic square formula - Revisited

Ramanujan's genius (r) was discovered by Hardy (l)

At a very young age Ramanujan designed the following formula for a 3 by 3 magic square:

C+Q | A+P | B+R
A+R | B+Q | C+P
B+P | C+R | A+Q

where A,B,C are integers in arithmetic progression and so are P,Q,R.


Rewriting Ramanujan's scheme somewhat to

2Q+R	|	2P+2R	|	P+Q
2P	|	P+Q+R	|	2Q+2R
P+Q+2R	|	2Q	|	2P+R

where P,Q,R are in the Rationals, it is clear that every (P,Q,R) yields a magic square with constant number 3 (P + Q + R).

I conjecture that for any 3 by 3 magic square a triple (P,Q,R) can be found in the Rationals such that they fit the above scheme. Finding a proof for this is one of my 'problems'. Naturally, I would be very interested in any counter-example.