Seven Conjectures in Geometry and Number Theory

TL;DR

This paper introduces seven new conjectures in geometry and number theory, generalizing well-known theorems and concepts, aiming to inspire further research in these mathematical fields.

Contribution

It proposes four synthetic geometry conjectures extending the Erdős–Mordell theorem and three number theory conjectures generalizing Fermat numbers.

Findings

Proposed four new conjectures in synthetic geometry.

Introduced three conjectures in number theory related to Fermat numbers.

Aimed to stimulate further mathematical investigation.

Abstract

In this short paper we propose four conjectures in synthetic geometry that generalize Erdos-Mordell Theorem, and three conjectures in number theory that generalize Fermat Numbers.