MathDB

P(m^n)+Q([0,k]) is composite for infinitely many k

Source: Bulgaria 1974 P2

June 20, 2021

Polynomialsnumber theory

Problem Statement

Let

f(x)

and

g(x)

be non-constant polynomials with integer positive coefficients,

m

and

n

are given natural numbers. Prove that there exists infinitely many natural numbers

k

for which the numbers

f(m^n)+g(0),f(m^n)+g(1),\ldots,f(m^n)+g(k)

are composite.
I. Tonov