Professor Who wants to develop a matrix$-$multiplication algorithm that is asymptotically

faster than Strassen$$s algorithm. Her algorithm will use the divide$-$and$-$conquer method, dividing each

matrix into n$/4\backslash$times n$/4$ submatrices, and the divide and combine steps together will take $\backslash$Theta $($n

$2$

$)$ time.

Suppose that the professor$$s algo creates a recursive subproblems of size n$/4.$ Whats the largest integer

value of a for which her algorithm could possibly run asymptotically faster than Strassen$$s$?$