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
For a mini-puzzle, scroll down to the bottom of this post…
A NEW SEQUENCE FOR THE OEIS!
Inspired by all that 82000 business (see HERE, HERE and HERE), I recently created another sequence centred on the idea of expressing numbers in different bases. Continue reading
While working on part two of the Pointless article, I wandered over to Twitter and stumbled upon the following problem:
Can a perfect square ever consist of the same string of digits written out twice (such as in 978978 or 46024602)? cc @jamestanton
— Matt Enlow (@CmonMattTHINK) December 4, 2014
This caught my imagination and I did a bit of an investigation. The results were unexpectedly interesting, involving a connection to a mysterious problem at the cutting edge of number theory and a trip off into the numerical stratosphere in search of some fairly large solutions.
You can read my account of the problem here. The maths used here is probably about first year undergraduate level, and the style is certainly more technical than the Pointless article, so come prepared.