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Pell and Pell-Lucas Numbers Associated with Brocard-Ramanujan Equation

Yıl 2017, Cilt: 7, 59 - 62, 19.12.2017

Öz

In this paper, the diophantine equations of the form $A_{n_{1}}A_{n_{2}}\cdots A_{n_{k}}\pm 1=B_{m}^{2}$ where $(A_{n})_{n\geq 0}$ and $(B_{m})_{m\geq 0}$ are either the Pell sequence or Pell-Lucas sequence are solved by applying the Primitive Divisor Theorem. This is another version of Brocard-Ramanujan equation.

Kaynakça

  • Berndt, B. C., Galway, W. F., On the Brocard-Ramanujan Diophantine equation $n!+1=m^{2}$, Ramanujan J., 4(1)(2016), 41--42.
  • Carmichael, R. D., \On the numerical factors of the arithmetic forms $\alpha ^{n}\pm \beta ^{n}$, Ann. of Math. Second S., 15(1/4)(1913), 30--48.
  • Dabrowski, A., On the Brocard-Ramanujan problem and generalizations, Colloq. Math., 126(1)(2012), 105--110.
  • Luca, F., The Diophantine equation $P(x)=n!$ and a result of M. Overholt, Glas. Math. Ser. III, 37(2)(2002), 269--273.
  • Marques, D., The Fibonacci version of the Brocard-Ramanujan diophantine equation, Portug. Math., 68(2011), 185--189.
  • Pongsriiam, P., Fibonacci and Lucas numbers associated with Brocard-Ramanujan equation, Commun. Korean Math. Soc., 32(3)(2017), 511--522.
  • Szalay, L., Diophantine equations with binary recurrences associated to Brocard-Ramanujan problem, Port. Math., 69(3)(2012), 213--220.
Yıl 2017, Cilt: 7, 59 - 62, 19.12.2017

Öz

Kaynakça

  • Berndt, B. C., Galway, W. F., On the Brocard-Ramanujan Diophantine equation $n!+1=m^{2}$, Ramanujan J., 4(1)(2016), 41--42.
  • Carmichael, R. D., \On the numerical factors of the arithmetic forms $\alpha ^{n}\pm \beta ^{n}$, Ann. of Math. Second S., 15(1/4)(1913), 30--48.
  • Dabrowski, A., On the Brocard-Ramanujan problem and generalizations, Colloq. Math., 126(1)(2012), 105--110.
  • Luca, F., The Diophantine equation $P(x)=n!$ and a result of M. Overholt, Glas. Math. Ser. III, 37(2)(2002), 269--273.
  • Marques, D., The Fibonacci version of the Brocard-Ramanujan diophantine equation, Portug. Math., 68(2011), 185--189.
  • Pongsriiam, P., Fibonacci and Lucas numbers associated with Brocard-Ramanujan equation, Commun. Korean Math. Soc., 32(3)(2017), 511--522.
  • Szalay, L., Diophantine equations with binary recurrences associated to Brocard-Ramanujan problem, Port. Math., 69(3)(2012), 213--220.
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Makaleler
Yazarlar

Dursun Taşçı

Emre Sevgi

Yayımlanma Tarihi 19 Aralık 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 7

Kaynak Göster

APA Taşçı, D., & Sevgi, E. (2017). Pell and Pell-Lucas Numbers Associated with Brocard-Ramanujan Equation. Turkish Journal of Mathematics and Computer Science, 7, 59-62.
AMA Taşçı D, Sevgi E. Pell and Pell-Lucas Numbers Associated with Brocard-Ramanujan Equation. TJMCS. Aralık 2017;7:59-62.
Chicago Taşçı, Dursun, ve Emre Sevgi. “Pell and Pell-Lucas Numbers Associated With Brocard-Ramanujan Equation”. Turkish Journal of Mathematics and Computer Science 7, Aralık (Aralık 2017): 59-62.
EndNote Taşçı D, Sevgi E (01 Aralık 2017) Pell and Pell-Lucas Numbers Associated with Brocard-Ramanujan Equation. Turkish Journal of Mathematics and Computer Science 7 59–62.
IEEE D. Taşçı ve E. Sevgi, “Pell and Pell-Lucas Numbers Associated with Brocard-Ramanujan Equation”, TJMCS, c. 7, ss. 59–62, 2017.
ISNAD Taşçı, Dursun - Sevgi, Emre. “Pell and Pell-Lucas Numbers Associated With Brocard-Ramanujan Equation”. Turkish Journal of Mathematics and Computer Science 7 (Aralık 2017), 59-62.
JAMA Taşçı D, Sevgi E. Pell and Pell-Lucas Numbers Associated with Brocard-Ramanujan Equation. TJMCS. 2017;7:59–62.
MLA Taşçı, Dursun ve Emre Sevgi. “Pell and Pell-Lucas Numbers Associated With Brocard-Ramanujan Equation”. Turkish Journal of Mathematics and Computer Science, c. 7, 2017, ss. 59-62.
Vancouver Taşçı D, Sevgi E. Pell and Pell-Lucas Numbers Associated with Brocard-Ramanujan Equation. TJMCS. 2017;7:59-62.