I'm having alot of trouble with the proof below. The parts I don't understand will be bolded, but I have written the whole proof so you can also follow the argument.

Let be non negative intgers. If , then

a) is a rational number whose denominator is a divisor of

b) is a rational number whose denominator is a divisor of

Where is the lowest common multiple of .

The proof is given as follows:

Let be any non-negative number. Consider the integral

(1)

Developinto a geometrical series and perform the double integration. Then we obtain

(2)

Assume that . Then we can write this sum as

If we putthen assertion a) follows immediately.If we differentiate with respect to and put , then integral (1) changes into

and summation (2) becomes

and assertion (b) now follows straight away.

Thank you thank you thank you to anyone who can explain those bolded sentences, I will be forever indebted to you!

Havelock (formerly HTale)