Find all positive integers x > y > z such that x²+27y, y²+27z, z²+27x and x²+y²+z²+27 are all perfect squares.

I don't know how to do this. It's surely not with the approach I've taken here. 

x^2+27y=192^2

y^2+27z=384^2

z^2+27x=744^2

unfortunately x^2+y^2+z^2+27 is not a perfect square. I can give different values to a and b and search again for new posible values of x, but would be time consuming... 

So, this is probably not the way to do this. 

Posted by armando on 2019-01-23 06:48:24