# An Identity for Vertically Aligned Entries in Pascal's Triangle

## TL;DR

This paper establishes a linear dependence among vertically aligned entries in Pascal's triangle and applies this mathematical insight to morphisms between hyperelliptic curves.

## Contribution

It introduces a novel linear dependence relation for Pascal's triangle entries and demonstrates its application in algebraic geometry involving hyperelliptic curves.

## Key findings

- Proves a linear dependence among vertically aligned Pascal's triangle entries
- Provides an application to morphisms between hyperelliptic curves
- Enhances understanding of combinatorial and algebraic structures

## Abstract

The classic way to write down Pascal's triangle leads to entries in alternating rows being vertically aligned. In this paper, we prove a linear dependence on vertically aligned entries in Pascal's triangle. Furthermore, we give an application of this dependence to morphisms between hyperelliptic curves.