For how many integers is the square of an integer?

Source: NCTM Mathematics Teacher

**SOLUTION**

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

Verification

Don’t forget the special value

There are values of for which is the square of an integer.

**Answer**:

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for n= 16 the equation would be [16/(20-16)] = 16/4 = 4 = 2^2 which is a perfect square. Hence the ans is 16.