Discrete Mathematics Prove or Disprove the following stateme

(Discrete Mathematics) Prove or Disprove the following statement: For all integer x 1 there exists an integer y such that xy = 6x + y

Solution

xy = 6x + y

xy - y = 6x

y(x-1) = 6x

y = 6x/(x-1)

For all integer x, y does not exist.

For example, when x= 5, y= 15/2 which is not an integer.

So, the given statement is not true and its proved.