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This book is now in its fourth edition the first was in , the fourth in , and another idiosyncratic feature is that it was updated not by revising the text but by adding a series of supplements; these now make up one-third of the book. The supplements deal with the same problems as in the main work, but usually in more depth, and they cover what were at time of publication some of the latest results.

My favorite part is the long discussion on the nature of conjectures beginning on p. That said, for the professional mathematician it is fascinating to see the interconnections in these many topics. A good introductory text where consideration of particular problems and numerical evidence drive the exposition is R.

## Progress in Guy's "Unsolved problems in Number Theory"? - MathOverflow

Allen Stenger is a math hobbyist and retired software developer. His mathematical interests are number theory and classical analysis.

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Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. What are the most interesting examples of unsolved problems in number theory which an 18 year can understand? A problem I particularly like is Broccard's problem. There are lots of Unsolved problems in number theory and some of them are not paid enough attention.

## Solved and Unsolved Problems in Number Theory

Try it if you want to! And give special thanks to the guy who implemented legendre in the GMP library :.

The title of your question is also the title of a fantastic book by Richard Guy. Get that book, and you'll never run out of good problems to think about.

Recent developments of the subject is very interesting. There is a paper very recently the claimed the proof of Goldbach weak conjecture:.

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Terrence Tao proved in that "Every odd number greater than 1 is the sum of at most five primes". I think nearly everything one does in number theory is understandable if you followed the story far enough. Even the most difficult to understand theorem usually makes sense in special cases if you understood the great theorems that came before it. But yeah there is a wealth of immediately understandable theorems in number theory that have gone unsolved so far.

There are also problems that have been solved My favourite of these is the congruent number problem. This asks which positive integers can be areas of right angled triangles with rational sides. In studying this problem you get to be led through a rich area of number theory upto modern day research on elliptic curves and modular forms. As mentioned above this problem has been solved Sign up to join this community.