This blog has a really interesting assortment of articles on mathematics and programming. You can use the tags to your right to find topics that interest you, or you may want to have a look at

- my Python articles about the core language; or
- the problems I wrote to get your brain working.

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Can you prove that there are arbitrarily many primes in arbitrarily big intervals?

Let's prove that if \(k\) is an integer, then \(\gcd(k, k+1) = 1\). That is, any two consecutive integers are coprime.

This simple problem is an example of a very interesting phenomenon: if you have a large enough "universe" to consider, even randomly picked parts exhibit structured properties.