# On the Diophantine Equation 1/a + 1/b = (q+1) / pq

## TL;DR

This paper completely solves the Diophantine equation 1/a + 1/b = (q+1)/pq for integers a, b, where p and q are primes with q+1 dividing p-1, using elementary techniques.

## Contribution

It provides a complete classification of solutions to a specific prime-related Diophantine equation with elementary methods.

## Key findings

- All solutions are explicitly characterized.
- The solutions depend on the divisibility condition q+1 | p-1.
- The approach avoids advanced number theory techniques.

## Abstract

Let $p$ and $q$ be distinct primes such that $q+1 | p-1$. In this paper we find all integer solutions $a$, $b$ to the equation $1/a + 1/b = (q+1)/pq$ using only elementary methods.