Master theorem: what to do with constant in parenthesis? In analysis of algorithms, we sometimes use the (unsimplified) Master Theorem for recurrence relations.
What should be done in the case that there is a constant factor in the numerator following T?
$$
T(n) = 2T\left(\frac{5n}{8}\right) + 1
$$
Does b simply equal $\frac{5}{8}$? This seems a contradiction to the Theorem.
Usually the general form of the recurrences solved by the Master theorem is stated as:
$$
T(n) = aT\left(\frac{n}{b}\right) + f(n).
$$
In your recurrence you have $a=2$, $b=\frac{8}{5}$, and $f(n)=1$.