Confirm the following properties of the greatest common divisor:(a) If gcd(a, b) = 1

Chapter 2, Problem 20

(choose chapter or problem)

Confirm the following properties of the greatest common divisor:(a) If gcd(a, b) = 1, and gcd(a, c) = 1, then gcd(a, be)= 1.[Hint: Because 1 =ax+ by= au+ cv for some x, y, u, v,1 =(ax+ by)(au + cv) = a(aux + cvx + byu) + bc(yv).](b) If gcd(a, b) = 1, and c I a, then gcd(b, c) = 1.(c) If gcd(a, b) = 1, then gcd(ac, b) = gcd(c, b).(d) If gcd(a, b) = 1, and c I a+ b, then gcd(a, c) = gcd(b, c) = 1.[Hint: Let d = gcd(a, c). Then d I a, d I c implies that d I (a+ b) - a, or d I b.](e) If gcd(a, b) = 1, d I ac, and d I be, then d I c.(f) If gcd(a, b) = 1, then gcd(a2, b2) = 1.[Hint: First show that gcd(a, b2) = gcd(a2, b) = l.]