Open Conjectures on Congruences

TL;DR

This paper compiles 100 open and some recently confirmed conjectures on number theory, particularly involving congruences and quadratic forms, aiming to inspire further research and problem-solving in the field.

Contribution

It provides a comprehensive collection of open conjectures on congruences, including some recently proven ones, serving as a resource for future research and problem-solving.

Findings

100 unsolved conjectures listed

Some conjectures have been recently confirmed

Offers prizes for proofs of select conjectures

Abstract

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while conjectures in Part B have been recently confirmed. We hope that this material will interest number theorists and stimulate further research. Number theorists are welcome to work on those open conjectures; for some of them we offer prizes for the first correct proofs.