For how many integers is the square of an integer?
Source: NCTM Mathematics Teacher
The square of an integer is a positive integer, therefore is a positive integer. If or , a contradiction. Thus, . If the numerator is positive, the denominator must also be positive
Furthermore, the numerator must be greater than or equal to the denominator for the rational number to be an integer
Don’t forget the special value
There are values of for which is the square of an integer.