Online Course Discussion Forum

MCIII Number Theory 4.2

 
 
Picture of Tina Jin
MCIII Number Theory 4.2
by Tina Jin - Saturday, 30 December 2023, 9:48 PM
 

Hello,


I tested random small numbers for this problem and got m as the answer. I don't know why this is true though, it just seems to be true from the numbers that I plugged in.

Is there a rigorous method to do this?


Thanks,

Tina Jin

 
Picture of Dr. Kevin Wang
Re: MCIII Number Theory 4.2
by Dr. Kevin Wang - Monday, 8 January 2024, 12:49 AM
 

I think the book contains the solution of this problem at the end.  If it is hard to follow, let $m=12$ and try to follow the solution with this particular value, and see if you can categorize the numbers $a$ between $1$ and $12$ and group them according to the value of $\gcd(a,m)$, and how many numbers are in each category, and how that is related with the question itself.