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.