Problem:
Consider the set of all fractions , where and are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by , the value of the fraction is increased by ?
Answer Choices:
A.
B.
C.
D.
E. infinitely many
Solution:
Because , it follows that and so . The only possible values of are , and because and are positive integers. Thus the possible values of are , and . Of the resulting fractions , and , only the first is in simplest terms.
The problems on this page are the property of the MAA's American Mathematics Competitions