MathDB

Tita the Frog sits on the number line. She is initially on the integer number

k>1

. If she is sitting on the number

n

, she hops to the number

f(n)+g(n)

, where

f(n)

and

g(n)

are, respectively, the biggest and smallest positive prime numbers that divide

n

. Find all values of

k

such that Tita can hop to infinitely many distinct integers.

Problem Statement