# Mathematics. Are you scared now?

Yes, this page contains some of the mathematical content of my own production -- usually somewhere in the area of recreational and/or educational.
## Problem Solving

Rado Harman once asked a quite interesting question (sorry, only in Slovak) on his blog. Being as stubborn as I am, I didn't give up until I was pretty sure I found the full solution (the proof has been updated on 2012/02/05 to fix some grammar and style mistakes).

Another time, I stumbled upon the Unsolved Problems and Rewards webpage of Prof. Clark Kimberling. Most of the problems looked both nice and challenging. In the end, a few pages of my notebook became victims of problem *7. The Mysterious B Sequence*… until the full picture emerged and the proof appeared in plain sight.

## Number crunching

Some problems are more suited for computers than humans. Another Peter asked us to prove that 1847^2013+2 is indeed a prime. Since this number is of general form, I used the excellent Primo program by Marcel Martin and let it run in the spare time for a few days. The result? Yes, the number is now a certified prime (you can check the certificate yourself and it is considerably faster than searching for the certificate).

## (Possibly) Educational Content

Apart from problem solving, I occasionally write a piece of text here or there on various subjects. One of them was a brief introduction to Banach spaces (Postscript format only) and their uses, aimed at students of Mathematical Analysis 3 (multivariable real analysis) at Faculty of Mathematics, Physics and Informatics of Comenius University.