Sur les courbes hyperelliptiques cyclotomiques et les équations
Wilfrid Ivorra
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Let p be a prime number ≥ 11 and c be a square-free integer ≥ 3. In this paper, we study the diophantine equation in the case where p belongs to 11,13,17. More precisely, we prove that for those primes, there is no integer solution (x,y,z) to this equation satisfying gcd(x,y,z) = 1 and xyz ≠ 0 if the integer c has the following property: if ℓ is a prime number dividing c then ℓ ≢ 1 mod p. To obtain this result, we consider the hyperelliptic curves and , where is the pth cyclotomic...