This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas, conjectures, and conclusions in writing. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory. The presentation begins by familiarizing students with typical examples that illustrate central themes, followed by numerous carefully selected problems and extensive discussions of their solutions. The book engages students in creative thinking and stimulates them to express their comprehension and mastery of the material beyond the classroom. 104 Number Theory Problems is a valuable resource for advanced high school students, undergraduates, instructors, and mathematics coaches preparing to participate in mathematical contests and those contemplating future research in number theory and its related areas.