Dear Seqfans, We have real plane in 3D Cartesian space x(1-a)+(a^2-a)y+(2-a^4)z=0 where a is single one real root of quintic polynomial a^5-a-1=0 Does exist on this plane rational points (different as od x=y=z=0) ? If not does existed points expressible by radicals (polynomial a^5-a-1 have not solvable Galois group S5 over rationals) Best wishes Artur