Number Theory Problem Watch
Ok, so let's start with another one as I promised
If x, y , z, k is positive integers so that
x^2 + y^2 + z^2 = k(xyz +1).
Prove there are 2 positive integers a and b so that k = a^2 + b^2
That's my 1st one.
Too tired to do this. Maybe tomorrow.
(10,2,1) gives k=5. It is key to realize that k must divide one of x,y,z (its clearly immaterial which). I've made considerable progress on the problem, but its still not finished.
It seems be harder with 3 variables(not contains k), not only 2 as Galois's question. Proving it ... haha ... I think I must quit cuz even 2 variables it did make me crazy.