# 1998 PMWC Problems/Problem I2

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## 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?

## Solution

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)