After considering this problem for a while it proved rather challinging. I started of by constructing a diophanite equation (An equation that the solutions have to be integers) and with the help of the computer found a formula for one of the 3 values in the pythagorian triple. The formula is in the form of a GIF and is uploaded with this solution. I feel, if my fomula is correct, which is has been for a far a I have tested it which is up to about n=100 but after that the values are too large for the computer to hand. To work out each triplet just put a value n into the fomula that is 2 or bigger and an integer and it will give the 2nd longest side. Here are my first few examples:
3 4 5
20 21 29
119 120 169
696 697 985
4059 4060 5741
23660 23661 33461
137903 137904 195025
803760 803761 1136689
4684659 4684660 6625109
27304196 27304197 38613965
159140519 159140520 225058681
927538920 927538921 1311738121
5406093003 5406093004 7645370045
31509019100 31509019101 44560482149
Solution
24493
Problem
First name
Sam Bealing
School
Bridgewater High School
Country
Age
11