April 2026
Problem of the Month
Triangular Numbers
Submitted by Davit Banana of Turkey
Think of a positive number 𝑛.
Add up all the numbers from 1 to n (this is called a triangular number).
When does the total form a perfect square?
For example:
If n=1, the sum is 1 -- a perfect square.
If n=4, the sum is 10 -- not a perfect square
If n=5, the sum is 15 -- not a perfect square
If n=49, the sum is 1225 -- a perfect square (352).
Can you find the first five numbers n where this happens (we have given you two of them)?