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
Develop into a geometrical series and perform the double integration. Then we obtain
Assume that . Then we can write this sum as
If we put then 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)