Fermat's last theorem : récent developments.
Let Fₙ be the Fibonacci sequence defined by F₀=0, F₁=1, . It is well known that for any odd prime p, where (-) denotes the Legendre symbol. In 1960 D. D. Wall [13] asked whether is always impossible; up to now this is still open. In this paper the sum is expressed in terms of Fibonacci numbers. As applications we obtain a new formula for the Fibonacci quotient and a criterion for the relation (if p ≡ 1 (mod 4), where p ≠ 5 is an odd prime. We also prove that the affirmative answer to...