 Therefore, the number of steps "T" may vary dramatically between neighboring pairs of numbers, such as T("a", "b") and T("a", "b" + 1), depending on the size of the two GCDs.The recursive nature of the Euclidean algorithm gives another equation

where "T"("x", 0) = 0 by assumption.If the Euclidean algorithm requires "N" steps for a pair of natural numbers "a" > "b" > 0, the smallest values of "a" and "b" for which this is true are the Fibonacci numbers "F""N"+2 and "F""N"+1, respectively.