provide handwriting solution to each question

Q1: (2 marks) 8b: (Without applying the Canonical form of a number n > 1 prove that for distinct prime numbers p, q ifplnandqlnthenpqln.) Q2: (2 marks) 8d: [Prove ifa s r (mod p) and a s r (mod p), then a s r (mod pq).] Q3: (3 marks) Be: [A number n between 4000 and 11000, when we divide it by 17 or by 19 or by 23 it leaves the remainder 14. Find all such numbers n. How many such numbers exist in this interval? (Hint: try to use a version of part (d).]