The author formulates a conjecture which implies Pillai's conjecture and a theorem of \textit{A. Schinzel} and \textit{R. Tijdeman} [Acta Arith. 31, 199-264 (1976; Zbl 0339.10018)] that for a polynomial with integer coefficients and at least two distinct roots, there are only finitely many perfect powers in its values at integral points. The author studies the relationship of generalised \(abc\) conjecture and his own conjecture. Some conjectures on the equation of Nagell-Ljunggren are formulated.