MathDB

Prove that: (a) If

(a_n)_{n\geq 1}

is a strictly increasing sequence of positive integers such that

\frac{a_{2n-1}+a_{2n}}{a_n}

is a constant as

n

runs through all positive integers, then this constant is an integer greater than or equal to

4

; and (b) Given an integer

N\geq 4

, there exists a strictly increasing sequene

(a_n)_{n\geq 1}

of positive integers such that

\frac{a_{2n-1}+a_{2n}}{a_n}=N

for all indices

n

Problem Statement