The chapter introduces 68 unsolved problems and conjectures in number theory, covering various topics such as additive representation functions, the Erdős–Fuchs theorem, multiplicative problems, additive and multiplicative Sidon sets, hybrid problems, arithmetic functions, the greatest prime factor function, and mixed problems. The author, András Sárközy, dedicates the paper to the memory of Paul Erdős and Paul Turán, reflecting on his own contributions to mathematics and the importance of fostering the next generation of mathematicians. The chapter also delves into additive representation functions, presenting results and open problems related to the monotonicity of these functions for different types of sets of non-negative integers.The chapter introduces 68 unsolved problems and conjectures in number theory, covering various topics such as additive representation functions, the Erdős–Fuchs theorem, multiplicative problems, additive and multiplicative Sidon sets, hybrid problems, arithmetic functions, the greatest prime factor function, and mixed problems. The author, András Sárközy, dedicates the paper to the memory of Paul Erdős and Paul Turán, reflecting on his own contributions to mathematics and the importance of fostering the next generation of mathematicians. The chapter also delves into additive representation functions, presenting results and open problems related to the monotonicity of these functions for different types of sets of non-negative integers.