# Tag Archives: rational number

## Values of Integers

If and are integers such that , what are the possible values of ? (a) only (b) only (c) only multiples of (d) any integer (e) none of these Source: NCTM Mathematics Teacher, September 2006 Solution Let be an integer … Continue reading

## Multiple of 3

If is an integer, show why must be a multiple of . Source: NCTM Mathematics Teacher, October 2006 Solution which is a rational number. Clearly, for to be an integer must be a multiple of . Answer: Shown in solution

## 2x^2=3y^2

What is the only pair of integers for which twice the square of the first equals three times the square of the second? Source: NCTM Mathematics Teacher, October 2006 Solution We are looking for integers such that . If , … Continue reading

## Divide in Half

Divide in Half How many ordered pairs of integers satisfy ? Source: NCTM Mathematics Teacher 2006 SOLUTION For to be an integer must divide evenly. ordered pairs satisfy the requirement: , and . But, I don’t know how to prove … Continue reading

## Square of an Integer

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 … Continue reading