How would you go about proving that
We know by the D.A. that
and
These equations imply that
and
Adding the first two gives:
If I could show that , I would be done, right? Since that would imply that is the remainder upond dividing by . How how do we know that for sure?
Thanks for any help,
james
Oh, I made algebraic mistake. It should be
kn+(a+b)=pn+qn+a+b
nk+(a+b)=n(p+q)+(a+b)
Now suppose that it was stated that k = p+q. I think it should be Okay since the first term on bothside give the same remainder, and it becomes
When k=p+q, (a+b)mod n = (a+b) mod n since bothside have multiple of n. Of course when , the LHS RHS.
Yah?