John D. Cook • 5/12/2026

Euler function

This article discusses the Euler function (specifically the Euler function defined by an infinite product) and its relationship to the probability that a random matrix over a finite field is invertible. It explains how the probability converges quickly as matrix size increases, and how the Euler function provides the limiting value. The post includes a Python script demonstrating rapid convergence, and touches on related concepts like the pentagonal number theorem and q-analogs.

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#Python #Euler Function #Pentagonal Number Theorem