Number Theory Assignment 7: Solutions for Number Theory Problems

This document presents the complete solutions to Number Theory Assignment 7. The assignment covers several key concepts in number theory. The first problem involves determining the solvability of a quadratic congruence using Euler's Criterion. The second problem presents a proof of Wilson's theorem, leveraging the existence of primitive roots. The third problem focuses on proving the number of primitive roots modulo m. The fourth problem delves into ElGamal public-key encryption, including its decryption process and security analysis. Additional problems explore primitive roots modulo prime powers and fifth roots of unity, and the lambda function. The document provides detailed explanations and proofs for each problem, offering a comprehensive understanding of the topics covered. It is a valuable resource for students studying number theory.