Arithmetic is where numbers run across your mind looking for the answer. Arithmetic is like numbers spinning in your head faster and faster until you blow up with the answer. KABOOM!! Then you sit back down and begin the next problem. (Alexander Nathanson) Number theory is an ancient subject, but we still cannot answer many simplest and most natural questions about the integers. Some old problems have been solved, but more arise. All the research for these ancient or new problems implicated and are still promoting the development of number theory and mathematics.