hi as for 1): let's say x,y, z>2 if x^2+y^2=c, we can choose z^2 = c-1 -this condition complies with 1)- c^2=x^4 + y^4 +2*x^2*y^2 => x^4 + y^4 = c^2 - 2*x^2*y^2 z^4= (c-1)^2 => z^4 = c^2 -2*c+1 let's check now: x^4 + y^4 > z^4 c^2 - 2*x^2*y^2 > c^2 -2*c+1 2*(c-x^2*y^2)>1 ----but c=...