Here is a nice problem tweeted by the Republic of Mathematics:

Average of 3 consecutive cubes, n^3, (n+1)^3, (n+2)^3 is an integer. Same true if 3 replaced by odd integer?

— Republic of Math (@republicofmath) August 4, 2015

Free of the constraints of Twitter’s 140 character limit, let’s explain this problem in a little more detail. Continue reading