On the irreducibility of f(2ⁿ,3ᵐ,X) and other such polynomials

Let f(t₁, …, tᵣ, X)∈ Z[t₁, …, tᵣ,X] be irreducible and let a₁, …, aᵣ∈ Z \0,± 1\. Under a necessary ramification assumption on f, and conditionally on the Generalized Riemann Hypothesis, we show that for almost all integers n₁, …, nᵣ, the polynomial f(a₁n₁, …, aᵣnᵣ, X) is irreducible in Q[X].