MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

How many integral solutions are possible for the equation $a_1 \times a_2 \times \ldots \times a_k = N$ where each of $a_1, a_2, \ldots, a_k$ satisfy the property $0 \leq a_i \leq 9$?
The question is to find out the number of possible combinations $(a_1, a_2, \dots, a_L)$ such that $(\frac{a_1}{a_2})(\frac{a_3}{a_4}) \dots = N$ with the constraint that $a_1, a_2, \dots ,a_3$ a_L$satisfy$0 \leq a_i \leq 9$. So, my approach was to consider$N$as$\frac{N}{1}, \frac{2N}{2}, \ldots$till$\frac{mN}{m}$such that$mN \leq 9^k, k = L - 1 or L$. Now, if I get the possible combinations for both numerator and denominator(for all these fractions), then I could multiply and add these combination numbers to get the final result. Can any other approach be adopted for doing it? 3 added 592 characters in body How many integral solutions are possible for the equation$a_1 \times a_2 \times \ldots \times a_k = N$where each of$a_1, a_2, \ldots, a_k$satisfy the property$0 \leq a_i \leq 9 $? The question is to find out the number of possible combinations$(a_1, a_2, \dots, a_L)$such that$(\frac{a_1}{a_2})(\frac{a_3}{a_4}) \dots = N$with the constraint that$a_1, a_2, \dots ,a_3$satisfy$0 \leq a_i \leq 9$. So, my approach was to consider$N$as$\frac{N}{1}, \frac{2N}{2}, \ldots$till$\frac{mN}{m}$such that$mN \leq 9^k, k = L - 1 or L\$. Now, if I get the possible combinations for both numerator and denominator(for all these fractions), then I could multiply and add these combination numbers to get the final result. Can any other approach be adopted for doing it?