Solutions of the Diophantine Equation 7X 2 + Y 7 = Z 2 from Recurrence Sequences
| Autor: | Hashim, Hayder R. |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
11d41
Polynomial diophantine equations Fibonacci number Lucas sequence General Mathematics Diophantine equation 010102 general mathematics 11b39 Quadratic reciprocity 01 natural sciences Combinatorics Integer Lucas number lucas sequences QA1-939 Congruence (manifolds) [MATH]Mathematics [math] pell equations 0101 mathematics Mathematics |
| Zdroj: | Communications in Mathematics, Vol 28, Iss 1, Pp 55-66 (2020) |
| ISSN: | 2336-1298 |
| DOI: | 10.2478/cm-2020-0005 |
| Popis: | Consider the system x 2 − ay 2 = b, P (x, y) = z 2, where P is a given integer polynomial. Historically, the integer solutions of such systems have been investigated by many authors using the congruence arguments and the quadratic reciprocity. In this paper, we use Kedlaya’s procedure and the techniques of using congruence arguments with the quadratic reciprocity to investigate the solutions of the Diophantine equation 7X 2 + Y 7 = Z 2 if (X, Y) = (L n , F n ) (or (X, Y) = (F n , L n )) where {F n } and {L n } represent the sequences of Fibonacci numbers and Lucas numbers respectively. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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