MathDB

4

Part of 2019 Switzerland Team Selection Test

Problems(1)

Another Sequence with P^n(x)

Source: Swiss TST 2019 P4

5/12/2020
Let pp be a prime number. Find all polynomials PP with integer coefficients with the following properties: (a)(a) P(x)>xP(x)>x for all positive integers xx. (b)(b) The sequence defined by p0:=pp_0:=p, pn+1:=P(pn)p_{n+1}:=P(p_n) for all positive integers nn, satisfies the property that for all positive integers mm there exists some l≥0l\geq 0 such that m∣plm\mid p_l.
number theorypolynomialprime numbersalgebra