Positional number systems typically have a integer base, but irrational and even complex bases are possible. The golden ratio was the first irrational base.

Powers of the golden ratio are nearly integers. This post explains why. Also, these integers are the sum of two Fibonacci numbers.

For any x, the behavior of multiples of x mod 1 is easy to classify. The powers of x mod 1 are more interesting. We give examples of different behavior.

How to calculate large powers of 3 + √2 numerically with bc and symbolically with Mathematica. Conjecture regarding the integer and irrational parts.

Moessner's Magic is a generalization of an ancient theorem that wasn't discovered until 1951.

You can find three primitive Pythagorean triangles with the same area, but what about four?

Testing the time to factor big integers in Python with SymPy compared to Matheamtica

Memorable prime numbers with various numbers of digits. For example, if you need a five-digit prime, you could say 18181.

A prime number that looks like a blackand-white image of an American flag when written in a block.

An ingenious device for factoring integers from the days before computers. A set of around 300 stencils could factor 9-digit numbers.