MathDB

For an infinite sequence

a_1<a_2<a_3<...

of positive integers we say that it is nice if for every positive integer

n

holds

a_{2n}=2a_n

. Prove the following statements:

a)

If there is given a nice sequence and prime number

p>a_1

, there exist some term of the sequence which is divisible by

p

b)

For every prime number

p>2

, there exist a nice sequence such that no terms of the sequence are divisible by

p

Problem Statement