MathDB

An infinite array of rational numbers

G(d, n)

is defined for integers

d

and

n

with

1\leq d \leq n

as follows:

G(1, n)= \frac{1}{n}, \;\;\; G(d,n)= \frac{d}{n} \sum_{i=d}^{n} G(d-1, i-1) \; \text{for} \; d>1.

For

1 < d < p

and

p

prime, prove that

G(d, p)

is expressible as a quotient s\slash t of integers

s

and

t

with

t

not divisible by

p.

Problem Statement