Testing pentagonal numbers

This article explains how to test whether a given number is a pentagonal number (ordinary or generalized) using the formula Pn = (3n² − n)/2. It covers rejecting non-pentagonal numbers by checking if 24x+1 is a perfect square, and provides a Python function using integer arithmetic to handle arbitrarily large numbers without floating-point precision issues. The article includes code examples for sqrt_floor and pentagonal_index functions, and demonstrates testing with large values like 2^127-1 and 10^200.