How do I go about proving the uniqueness of an existing solution to a recurrence equation of the form
$$ a_{n+1} - f(n)a_n = 0 $$ ?
Is there a theorem related to questions of uniqueness and existence for recurrence relations of a certain type as is the case for ordinary differential equations?
Hint
If the recurrence equation is of the form $$a_{n+1} - f(n)a_n = 0$$ you could easily show that the solution is simply given by $$a_n=c \prod _{i=1}^{n-1} f(i)$$