Exercise 26. Let m, ai, bi, 22,62 € Z. Suppose that a = bi mod m and a2 = b2 mod m. (a) Prove that ai + a2 = b + b2 mod m. (b) Prove that a = b b mod m. (Hint: Since ai bimod m m divides bi-diso for some integer k, we have b - ai = km, so b = a1 + km. Similarly, for some integer , we have b2 = 22 + m.)
