Suppose that the statement is correct.
Let and .
Then so that a and b satisfy the hypothesis of the statement.
By the statement, there exists an integer z such that .
Then by substitution.
Subtracting 1.5 from both sides: .
But is not an integer.
Thus, z is both an integer and not an integer, a contradiction.
The hypothesis must be false and the statement is false, which was to be shown.