Append the digit 1 to the end of every triangular number. For instance, from 3 you’d get 31, and from 666 you’d get 6,661. Now take a look at all of the divisors of the numbers you’ve created. What are the units digits of the divisors for every number created in this way? Can you prove that this result always holds?
Just for fun I have dubbed these numbers — the ones you get by appending a unit to triangular numbers — the triangunit numbers. I’ve found a pattern and even checked it for the first 10,000 triangular numbers using a computer, but so far a proof has eluded me!
By the way, the triangunit numbers are sequence A062786 in the Online Encyclopedia of Integer Sequences, but that page contains a spoiler (I think, I didn’t read it) so don’t peek if you want to figure it out yourself!