Displaying similar documents to “Power values of certain quadratic polynomials”

On D 5 -polynomials with integer coefficients

Yasuhiro Kishi (2009)

Annales mathématiques Blaise Pascal

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We give a family of D 5 -polynomials with integer coefficients whose splitting fields over ℚ are unramified cyclic quintic extensions of quadratic fields. Our polynomials are constructed by using Fibonacci, Lucas numbers and units of certain cyclic quartic fields.

Markoff numbers and ambiguous classes

Anitha Srinivasan (2009)

Journal de Théorie des Nombres de Bordeaux

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The Markoff conjecture states that given a positive integer c , there is at most one triple ( a , b , c ) of positive integers with a ≤ b ≤ c that satisfies the equation a 2 + b 2 + c 2 = 3 a b c . The conjecture is known to be true when c is a prime power or two times a prime power. We present an elementary proof of this result. We also show that if in the class group of forms of discriminant d = 9 c 2 - 4 , every ambiguous form in the principal genus corresponds to a divisor of 3 c - 2 , then the conjecture is true. As a result, we obtain criteria...

Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields

Marcin Mazur, Stephen V. Ullom (2008)

Journal de Théorie des Nombres de Bordeaux

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We investigate as Galois module the unit group of biquadratic extensions L / M of number fields. The 2 -rank of the first cohomology group of units of L / M is computed for general M . For M imaginary quadratic we determine a large portion of the cases (including all unramified L / M ) where the index [ V : V 1 V 2 V 3 ] takes its maximum value 8 , where V are units mod torsion of L and V i are units mod torsion of one of the 3 quadratic subfields of L / M .

On the diophantine equation x 2 + 5 k 17 l = y n

István Pink, Zsolt Rábai (2011)

Communications in Mathematics

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Consider the equation in the title in unknown integers ( x , y , k , l , n ) with x ≥ 1 , y > 1 , n ≥ 3 , k ≥ 0 , l ≥ 0 and gcd ( x , y ) = 1 . Under the above conditions we give all solutions of the title equation (see Theorem 1).