2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66787In this paper two conjectures are proposed based on which we can prove the first case of Fermat's Last Theorem(FLT) for all primes $p \equiv -1 (\bmod~6)$. 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 $\leq 2437$ and Conjecture2 for primes $\leq 100003$.5 pagesHistory and Overviewtext