I got a little but of idea for the second one...
if a = b(mod n) and c = d(mod n), then ac = bd(mod n).
So, by using the definition of the modulus:
a = b + nk and c = d + nl for some integers we'll call k and l.
So by multiplying both of these conditions we then get:-
ac = (b + nk)(d + nl)
= bd + nkd + nlb + n^2kl
= bd + n(kd + lb + nkl)
which means that ac = bd(mod n) since (kd + lb + nkl) is just some
I hope this is right!
I did the similar operation for 1st but I am still not sure on how to resolve it?
coz I keep getting the some random terms in there...
Thanks for the any help!