Show that: if a = b(mod n) and C = d\modn), then a +c =b+d\mod n)!

Show that ()-{ = 1 -1 if q = ±1 mod 12 if q = ±5 mod 12

Let n1, n2, n3 be three numbers that are pairwise relativelyprime so that (n1, n2) = (n2, n3) = (n1, n3). Let a1, a2, and a3 be any integers.We showed in class that the systemx ≡ a1 (mod n1)x ≡ a2 (mod n2)x ≡ a3 (mod n3)has a unique solution, say b, modulo n1n2n3. Give a formula for b in terms ofa1, a2, a3, n1, n2, and n3. You will need to make use of multiplicative inverses.

Prove that if a + x ≡ a +y (mod n), then x ≡y (mod n)   details plz