Hi, how do you hunt for the number of solutions of :
Here is the solution:
Clearly, if we find this set, afterwards, there is only way of distribution, since the order is fixed.
Say, amongst the set , the integer comes times, then:
We know that the number of the solutions of this typical equation is , hence , the set is chosen, and hence the required number of solutions of the original equation is also .
_Below is an interesting problem: _
We want to create a Divisible Sequence of length from a number . In a Divisible Sequence, every term (except the starting number) is a divisor of the previous term. Examples of Divisible Sequences of length starting with are:
For primes , obtain an expression for the number of divisible sequences starting with , of length .
Note: You might leave this expression in a sum or a product form.