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 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

**Alternative solution
**

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