This is my math homework, do question 13, thanks.

2 of 3 O Math 109 SS1 2020 Homework 4 Lec A Prof. Chow #13. (a) Let p and q be distinct primes. Prove that if p divides r and q divides r, then pq divides r. Ilint: p and q are coprime. How can you apply Theorem 17.3.2? (b) Prove by induction on & that if pi, . . . , PR are distinct primes and a is an integer such that each p; divides r, then p1 . . . PR divides r. (c) Suppose that PI, .. ., PR are distinct primes. Prove that p . . . Px divides y if and only if PI . . . PK divides y?. (d) Disprove the following statement: If p is a prime and p2 divides y?, then p divides #14. (a) Prove that if p is a prime. then VD is irrational. Hints Proof by contradiction. (b) Generalize part (a) by proving that if pr. De are distinct primes, then VPIPE D