Problems in elementary number theory igor kortchemski. Sierpinski, 250 problems in elementary number theory, american elsevier, new york, 1970. There is, in addition, a section of miscellaneous problems. In this hand out, i provide some very key results in elementary number theory that it would be prudent to. The problems are brilliant and the solutions are very nice. Introduction number theory is a beautiful branch of mathematics. Prove that there exist an infinite number of ordered pairs a, b of integers such that.
If you want some challenging problems, try the starred questions in this book. Waclaw sierpinski 250 problems in elementary number theory presents problems and their solutions in five specific areas of this branch of mathe matics. Hint below, dont read if you want to solve it hint. I would like to put together a list of visually striking quite vague, i know, i dont expect everybody to agree on a definition of this mathematical objects, such as lorenzs attractor, mandelbrots set as an example for fractals, but please share more, if you know of any, hopf fibration etc my main purpose is to be able to show some of these to someone whos not. Just solved it, but since im on mobile i cant type it out and idk how to do spoiler tags. This book, the second of three related volumes on number theory, is the. This book presents the principal ideas of classical elementary number theory. Share 250 problems in elementary number theory, sierpinski. A huge chunk of number theory problems are diophantine equations named. Number theory is replete with sophisticated and famous open problems. A prime number is a positive integer p 1 such that if p divides ab then p divides.
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