MathDB

(a) Divide the line segment

[0,1]

into smaller black and white segments so that, for any polynomial

p(x)

of degree no greater than two, the sum of increments of

p(x)

along all the black segments is equal to that along the white ones. (The increment of

p(x)

along the segment

[a, n]

is the number

p(b) - p(a)

.)
(b) Can this be done for all polynomials of degree no greater than

1995

?
(Burkov)

Problem Statement