P3.1.8 (uses Java) Using the Least Number Axiom of Excursion 1.2, prove carefully that the factor method given in the text correctly factors any natural. (Hint: Assume that n is the small-est number that it doesnt factor correctly, trace the method with input n, and derive a contradiction.)

public void factor (natural x) { // prints sequence of prime factors of x, one per line // special cases: outputs empty sequence if x is 0 or 1 if (x = x) d = x;} System.out.println(); factor (x/a);} public void factor (natural x) { // prints sequence of prime factors of x, one per line // special cases: outputs empty sequence if x is 0 or 1 if (x = x) d = x;} System.out.println(); factor (x/a);}