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 ◄ −1(mod 6). With Pollaczek's result [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 ¶ 2437 and Conjecture2 for primes ¶ less than 100003.

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