Sorry for the picture PLz step by step a b c d epsilon Z en

Sorry for the picture!

PLz step by step

a, b, c, d epsilon Z en n epsilon N, n greaterthanorequalto 2. given that a b (mod n) c d (mod n). prove that ac bd (mod n).

Solution

a=b mod n

Hence,a-b=kn , for some integer k

a=b+kn

c=d+pn , for some integer p

ac=(b+kn)(d+pn)=bd+pbn+kdn+kpn^2=bd mod n

HEnce,

ac=bd mod n

Hence proved