First Case of Fermat's Last Theorem

Abstract

In this paper two conjectures are proposed based on which we can prove the first case of Fermat's Last Theorem(FLT) for all primes $p\equiv -1(\mathrm{mod}6)$. With Pollaczek's result {\bf [1]} and the conjectures the first case of FLT can be proved for all primes greater than 3. With a computer Conjecture1 was verified to be true for primes $\le 2437$ and Conjecture2 for primes $\le 100003$.

5 pages