,
are all polynomials such that ![\[ P(x^5)+xQ(x^5)+x^2R(x^5)=(x^4+x^3+x^2+x+1)S(x),\]](http://latex.artofproblemsolving.com/1/6/a/16a71abc110ece558d427a07d7be2d1f72148024.png)
prove that 
is a factor of 
.
such that the equality 
holds for all pairs of real numbers 
.
is an obvious solution. Now, let 
.
or 
.
.
Y by Adventure10, Mango247
The altitudes 
of a tetrahedron 
intersect in the center 
of the sphere inscribed in the tetrahedron 
. Prove that the tetrahedron is regular.
(D. Tereshin)
of a tetrahedron 
intersect in the center 
of the sphere inscribed in the tetrahedron 
. Prove that the tetrahedron is regular.(D. Tereshin)
