Problem:
Define an ordered quadruple of integers to be interesting if and . How many interesting ordered quadruples are there?
Solution:
For a given value of , an ordered quadruple is interesting if and only if it has the form with , and . The number of ordered triples meeting these conditions for , and is , and , respectively, and the number of possible values of is . Thus the number of interesting ordered quadruples is .
The problems on this page are the property of the MAA's American Mathematics Competitions