MathDB

Consider the equation

\frac{xy-C}{x+y}= k ,

where all symbols used are positive integers. 1. Show that, for any (fixed) values

C, k

this equation has at least a solution

x, y

; 2. Show that, for any (fixed) values

C, k

this equation has at most a finite number of solutions

x, y

; 3. Show that, for any

C, n

there exists

k = k(C,n)

such that the equation has more than

n

solutions

x, y

1