(257) 1

Part of 1990 Tournament Of Towns

Problems(1)

TOT 257 1990 Spring A S1 P(x) divisible by (x-1)^n

Source:

Prove that for all natural

n

there exists a polynomial

P(x)

(x-1)^n

such that its degree is not greater than

2^n

and each of its coefficients is equal to

1

0

-1

.
(D. Fomin, Leningrad)

algebrapolynomial