The Exceptional Selfcondensability of Powers of Five

TL;DR

This paper demonstrates that powers of five can be expressed arithmetically using their decimal digits and can contain arbitrarily long sequences of zeros.

Contribution

It introduces a novel property of powers of five, showing their self-condensability and zero-insertion capabilities in decimal form.

Findings

Any power of five can be expressed arithmetically with its decimal digits.

Powers of five can contain arbitrarily long sequences of zeros.

The paper establishes new properties of decimal representations of powers of five.

Abstract

We show any power of five may be expressed arithmetically with the digits of its decimal representation. We also show powers of five (in decimal) contain any amount of zeros in a row.