If and are integers such that , what are the possible values of ?
(c) only multiples of
(d) any integer
(e) none of these
Source: NCTM Mathematics Teacher, September 2006
Let be an integer such that . We have the following two equations
Multiply Eq. by and add to Eq.
Divide both sides by
For to be an integer, must be a multiple of .
Answer: (c) only multiples of