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Five squares in arithmetic progression over quadratic fields

Enrique González-Jiménez and Xavier Xarles

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Data (MAGMA and SAGE files)

• Corollary 21 (L_200_1000000.mg) MAGMA
• Corollary 33
  - precomputation.mg MAGMA --> L.sage
  - First Sieve: function to sieve the values that do not satisfy conditions on Proposition 6 and Corollary 21: FirstSieve.sage SAGE
  - D<10^13 that have passed the first sieve: L10a13.mg (1048)
  - Second Sieve: function to sieve the values that do not satisfy conditions on the Mordell-Weil sieve on section 6: SecondSieve.mg MAGMA
  - D<10^13 that have passed the first sieve and the second sieve for the primes less than 100: L2.sage (34)
  - Last Sieve: Function to compute the number of representation of an integer by the ternary quadratic forms 3x^2+9y^2+16z^2 and x^2+3y^2+144z^2 from Proposition 15. By Gonzalo Tornaria rep_tern.pyx SAGE
  - For each D from L2.sage number of representation of D by 3x^2+9y^2+16z^2 and x^2+3y^2+144z^2. data
  
• Function to construct an arithmetic progression of five square over a quadratic field coming from a point of the elliptic curve E^(1) : y^2=x(x+2)(x+6) AP5.mg MAGMA

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