Answer to Question #23210 in Combinatorics | Number Theory for Christopher Parrish

Question

Let us define the height h(a) of an integer a >= 2 to be the greatest n such that Euclid's algorithm requires n steps to compute gcd(a, b) for some positive b < a. Show that h(a) = 1 if and only if a = 2, and find h(a) for all a <= 8.