MathDB

Let

n

be a positive integer and let

a_n

be the number of ways to write

n

as a sum of positive integers, such that any two summands differ by at least

2

. Also, let

b_n

be the number of ways to write

n

as a sum of positive integers of the form

5k\pm 1

k \in Z

. Prove that

\frac{a_n}{b_n}

is a constant for all positive integers

n

5.1