Discrete Math
posted by Samantha on .
Let a, b, c, and d be integers, and let n be a positive integer. Prove that if a is congruent to c mod n and b is congruent to d mod n, then (ab) is congruent to (cd) mod n

Given:
a≡c mod n
b≡d mod n
Prove that (ac)≡(bd) mod n.
Let
a=kn+r ... k,r ∈ ℤ^{+}
c=ln+r ... l,r ∈ ℤ^{+}
Subtract:
(ac)=(kl)n
Similarly,
(bd)=(pq)n ... p,q ∈ ℤ^{+}
Therefore
(ac)≡(bd) mod n