1998 PMWC Problems/Problem I2
Triangular numbers and Square numbers can be represented in the following manner:
Find a pair of consecutive Triangular Numbers and the difference between a pair of consecutive Square Numbers whose difference are both 11. What is the sum of these four numbers?
We want or for . Therefore the two square numbers are and .
The th triangular number is equal to . Therefore we want or . Solving gives so our two numbers are and .
The sum of all our numbers is therefore .
(Credit to 54math for the solution here)