PLEASE SHOW DETAIL WILL RATE LIFESAVER if done so!! Let a, b, and c be integers, let n be a natural number, and suppose ged(c, n ) = 1. If ac = be (mod n). then a = b (mod n). Solution Given, gcd(c,n) = 1 So, c and n has no common multiples. Given, ac = bc (mod n) So, ac = nk + bc c(a - b) = nk so nk is a multiple of c. but gcd(c,n) = 1 so, k is a multiple of c Let k = cl ac = ncl + bc a = nl + b a = b (mod n) Hence proved.