Originally Posted by

**Havelock**
Let

be non negative intgers. If

, then

a)

is a rational number whose denominator is a divisor of

.

here should be

Let

be any non-negative number. Consider the integral

(1)

**Develop** **into a geometrical series and perform the double integration. Then we obtain** (2)

we have

put this in (1) and integrate the sum term by term to get (2).

Assume that

. Then we can write this sum as

**If we put ** ** then assertion a) follows immediately.** if we put we'll get: where now since and

we have also since we have thus

If we differentiate with respect to

and put

, then integral (1) changes into

and summation (2) becomes

**and assertion (b) now follows straight away**.

exactly the same argument as above but this time and thus the denominator will divide