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His argument shows that there are infinitely many solutions to Eulerís equation. In conclusion, although there has been some success in the last fifty years in limiting the number of rational points on varieties, there are still almost no methods for finding such points. It is to be hoped that a proof of the Birch and Swinnerton- Dyer conjecture will give some insight concerning this general problem. References If a compact three-dimensional manifold M3 has the property that every simple closed curve within the manifold can be deformed continuously to a point, does it follow that M3 is homeomorphic to the sphere S3? coset space SO(3)/I60 where SO(3) is the group of all rotations of Euclidean 3-space and where I60 is the subgroup consisting of the 60 rotations that carry a standard icosahedron to itself. The fundamental group 1(M3), consisting of all homotopy classes of loops from a point to itself within M3, is a perfect group of order 120. Brightning Principle Actually,natural light can be divided into single corresponding light wave of red,orange,yellow,green,blue,black and violet whthin 380-760nm.But it is not necessary to have so many kinds of lingt with different waves to synthetize white light.On TV screen,only three colours of loght are needed to synthetize white light ln fact,only two kinds of proper light waves which are intercomplementary colors can also synthetize white light suchas blue and yellow,red and blue grenn.When illuminated,materials(fabric,plastics,etc)can absorb blue light,reflect yellow light,and therefore we see yellow not white light.Fluorescent brightener can absorb ultraviolet light and send out white and blue light ,and so blue light and original yellow light are complementary colors conse-quently,we see white light.This is the brightening pringciple of fluorescent brightenenr.