For how many set of natural number values of x and y, (xy^2)+y+7 will divide (x^2)y+x+y?
A)0
B)1
C)2
D)5
E)None of these
A)0
B)1
C)2
D)5
E)None of these
Let's say that n is a positive integer. We're given that
(x²y + x + y) / (xy² + y + 7) = n
or
x²y + x + y = nxy² + ny + 7n
Now notice that this will always be true if x = 7n² and y = 7n.
So we can simply pick a natural value of n and always find a solution. For instance, if n = 1, then x = 7, y = 7. If n = 2, then x = 28, y = 14, etc.
With that, we have an infinite number of sets of natural numbers {x, y}.
