Problem:
Let , and be distinct integers such that
What is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If 45 is expressed as a product of five distinct integer factors, the absolute value of the product of any four is at least , so no factor can have an absolute value greater than 5 . Thus the factors of the given expression are five of the integers , and . The product of all six of these is , so the factors are , and 5 . The corresponding values of , and are , and 1 , and their sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions