Professor Caesar wishes to develop an integer-multiplication algorithm that is asymptotically faster than Karatsuba’s O(n log2 3 ) algorithm. His algorithm will use the divide-andconquer method, dividing each integer into pieces of size n/4, and the divide and combine steps together will take O(n) time. He needs to determine how many subproblems his algorithm has to create in order to beat Karatsuba’s algorithm. If his algorithm creates a subproblems, then the recurrence for the running time T(n) becomes T(n) = aT(n/4) + n. What is the largest integer value of a for which Professor Caesar’s algorithm would be asymptotically faster than Karatsuba’s algorithm? Justify your answer.