MathDB

different parities of number of prime divisors of adjacent members of an AP

Source: Macedonian TST 2022, P5

May 21, 2022

number theory

Problem Statement

Given is an arithmetic progression {

a_n

} of positive integers. Prove that there exist infinitely many

k

, such that

\omega (a_k)

is even and

\omega (a_{k+1})

is odd (

\omega (n)

is the number of distinct prime factors of

n

\textit {Proposed by Viktor Simjanoski and Nikola Velov}