A sum of 2 squares can be a square, eg. $3^2+4^2=5^2$.
A sum of 3 squares can be a square, eg. $3^2+4^2+12^2=13^2$, but is it possible to find an example where sum of any two of them would also be a square?
What about 4 squares such that sum of any two, any three and all four are squares?
Are there arbitrarily long sequences of squares such that any sum among them is a square?