2

Part of 1998 Kurschak Competition

Problems(1)

Polynomial in Z[x] - values at 1,...,n are powers of 2

Source: Kürschák 1998, problem 2

Prove that for every positive integer

n

, there exists a polynomial with integer coefficients whose values at points

1,2,\dots,n

are pairwise different powers of

2

algebrapolynomialalgebra unsolved