DUE DATE:
September 12, 2000(The rules are just that you do this on your own: it's not meant to be a group project.)
Consider the set of numbers {1, 3, 8}. This set has the following property:
(P) If you multiply two different numbers in the set and then add 1, you always get a square (of an integer).
For example,
1 • 3 + 1 = 4 = 22; 1 • 8 + 1 = 9 = 32; 3 • 8 + 1 = 25 = 52.
Your project:
1. Find the next smallest integer x that can be added to the set, still maintaining the property (P). Explain how you got your answer and verify your answer.
2. (Open ended) Explore any further integers that can be added to the set, still maintaining the property (P).