Finally it has been investigated solvability of the Pell equation $x^2-py^2=\mp q$ for the primes p and q.
📌 3 Key Takeaways
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Objective & Hypothesis:It has been obtained a theorem so that the class number to be one of the real quadratic field the type of which the wide Richauct Degert for the p and q primes satisfying p=(2q-1)^2, $(q\not\equiv3(mod 4))$.
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Key Findings & Data:It has been obtained a theorem so that the class number to be one of the real quadratic field the type of which the wide Richauct Degert for the p and q primes satisfying p=(2q-1)^2, $(q\not\equiv3(mod 4))$.
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Conclusion & Impact:Finally it has been investigated solvability of the Pell equation $x^2-py^2=\mp q$ for the primes p and q.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
It has been obtained a theorem so that the class number to be one of the real quadratic field the type of which the wide Richauct Degert for the p and q primes satisfying p=(2q-1)^2, $(q\not\equiv3(mod 4))$. Finally it has been investigated solvability of the Pell equation $x^2-py^2=\mp q$ for the primes p and q.
Özet
p ve q ,$(2q-1)^2-2$, $(q\not\equiv3(mod 4))$ sağlayan asallar olmak üzere, bu p ve q değerine karşılık gelen geniş (wide) Richaut Degert tipinden reel kuadratik sayı cisminin sınıf sayısının 1 olması için bir teorem elde edilmiş ve bunun sonucunda aynı p ve q değerleri için $x^2-py^2=\mp q$ Pell Denkleminin çözülebilirliği irdelenmiştir.
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Cite This Article
PEKİN, A. (2005). The class number of the real quadratic field Q $(\sqrt{p})$ and the solvability of the pell equation $x^2-py^2=\mp q$ for the prime p= $(2q-1)^2-2$. Trakya Üniversitesi Fen Bilimleri Dergisi, Cilt: 6 - Sayı: 1, 113–115. https://ajindex.com/articles/368878
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