Determine all possible real quadruplet(s) (P, Q, R, S) with P ≤ Q ≤ R ≤ S that satisfy this system of equations:

P + Q*R*S = 2, and:

Q + R*S*P = 2, and:

R + P*Q*S = 2, and:

S + P*Q*R = 2.

(In reply to re: Unreal! by Ady TZIDON)

Well yes, I was just having fun with the title.  My assertion was that all solutions are integral. 

My suspicion does not, on 2nd thought, look correct.

For instance:

P + QRS = 3
Q + PRS = 3
R + PQS = 3
S + PQR = 3

has a irrational solution where P = Q = R = S, and P + P^3 = 3.

What it think is instead true is that if the solution is rational, then it is integral.

Posted by Steve Herman on 2008-09-01 20:02:20