Browsing by Author "Chalupka, Karolina"

Filter results by typing the first few letters
Now showing 1 - 1 of 1
  • No Thumbnail Available
    Publication
    On a class of generalized fermat equations of signature (2, 2n, 3)
    (Academic Press Inc Elsevier Science, 2022-01-25) Chalupka, Karolina; Dabrowski, Andrzej; Soydan, Gokhan; SOYDAN, GÖKHAN; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; M-9459-2017
    We consider the Diophantine equation 7x(2) + y(2n) = 4z(3). We determine all solutions to this equation for n = 2, 3, 4 and 5. We formulate a Kraus type criterion for showing that the Diophantine equation 7x(2) + y(2p) = 4z(3) has no nontrivial proper integer solutions for specific primes p > 7. We computationally verify the criterion for all primes 7 < p < 10(9), p &NOTEQUexpressionL;13. We use the symplectic method and quadratic reciprocity to show that the Diophantine equation 7x(2) + y2p = 4z3 has no non-trivial proper solutions for a positive proportion of primes p. In the paper [10] we consider the Diophantine equation x(2) + 7y(2n) = 4z(3), determining all families of solutions for n = 2 and 3, as well as giving a (mostly) conjectural description of the solutions for n = 4 and primes n >= 5.