A Study of Kummer's Proof of Fermat's Last Theorem for Regular Primes

We study Kummer's approach towards proving the Fermat's last Theorem for regular primes. Some basic algebraic prerequisites are also discussed in this report, and also a brief history of the problem is mentioned. We review among other things the Class number formula, and use this formula to conclude our study.Comment: 11 page

A study of the crank function in Ramanujan's Lost Notebook

In this note, we shall give a brief survey of the results that are found in Ramanujan's Lost Notebook related to cranks. Recent work by B. C. Berndt, H. H. Chan, S. H. Chan and W. -C. Liaw have shown conclusively that cranks was the last mathematical object that Ramanujan studied. We shall closely follow the work of Berndt, Chan, Chan and Liaw and give a brief description of their work.Comment: 12 pages, version 3, to appea