Euclidean algorithm
Number of steps

The number of steps to calculate the GCD of two natural numbers, a and b, may be denoted by T (a, b). If g is the GCD of a and b, then a = mg and b = ng for two coprime numbers m and n. Then

as may be seen by dividing all the steps in the Euclidean algorithm by g. By the same argument, the number of steps remains the same if a and b are multiplied by a common factor w: T (a, b) = T (wa, wb). 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.
punctuation:no_comma, change_case:capital_word_frequency[7]