Diophantine equations connected to the Komornik polynomials

Abstract

We investigate the power and polynomial values of the polynomials Pn(X) = ∏ n k=0 ( X2·3 k − X3 k − 1 ) for n ∈ N. We prove various ineffective and effective finiteness results. In the case 0 ≤ n ≤ 3, we determine all pairs x, y of integers such that Pn(x) = y2 or Pn(x) = y3.