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Dergiler / Turkish Journal of Mathematics and Computer Science / 2017 / Volume: 7

Primes of the Form 4m + 1

Öznur Öztunç Kaymak(BALIKESİR ÜNİVERSİTESİ)0000-0003-3832-9947
Sayfa
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Yayın Tarihi
2017-12-19
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

From this equation, the problem of existing infinitely many primes exist p such that p =1 (mod4) of elemantary number theory is obtained.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper a new equation related to the sums of the squares of the first n k-Fibonacci numbers has been found.
📊
Temel Bulgular & Veri:In this paper a new equation related to the sums of the squares of the first n k-Fibonacci numbers has been found.
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Sonuç & Katkı:From this equation, the problem of existing infinitely many primes exist p such that p =1 (mod4) of elemantary number theory is obtained.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:k-Fibonacci number · Prime numbers

Abstract

In this paper a new equation related to the sums of the squares of the first n k-Fibonacci numbers has been found. From this equation, the problem of existing infinitely many primes exist p such that p =1 (mod4) of elemantary number theory is obtained.

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Bu Makaleye Atıf Yap

Kaymak, Ö. Ö. (2017). Primes of the Form 4m + 1. Turkish Journal of Mathematics and Computer Science, Volume: 7. https://ajindex.com/articles/1324956

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Kaynakça (8)

  1. Bolat, C., Köse, H., On the Properties of k-Fibonacci Numbers, Int. J. Contemp. Math. Sciences, 5, (2010), 1097-1105.
  2. Hoggat, V., Long, C., Divisibilty Properties of Generalized Fibonacci Polynomials, Fibonacci Quart. 12, 10M05, (1974), 113-120.
  3. Falcon, S., On the k-Lucas numbers, Int. J. Contemp. Math. Sci. 6, (2011), 21-24.
  4. Kalman, D., Mena, R., The Fibonacci Numbers-Exposed, Math. Mag. 76, no. 3, (2003), 167-181.
  5. Kilic, E., Sums of the squares of terms of sequence fUng, Proc. Indian Acad. Sci. (Math. Sci.) 118, (2008), 27-41.
  6. Koshy, T., Fibonacci and Lucas Numbers with Applications, Wiley, 2001.
  7. Ozgur, N. Y., Kaymak, O. O., On determination of k-Fibonacci and k-Lucas numbers, Math. Sci. Appl. E-notes, 3(2015), 20-26.
  8. Robbins, N., On Fibonacci Numbers and Primes of the form 4k + 1, The Fibonacci Quarterly 32, (1994), 15-16.