Persamaan Diophantine Tipe Ramanujan-Nagell x2 = yn + 2185

Mans L. Mananohas

Abstract


Dalam tulisannya di tahun 2014, Ulas mengajukan sebuah konjektur mengenai solusi bilangan bulat positif dari persamaan Ramanujan-Nagell x2 = yn + 2185. Di sini penulis termotivasi untuk melakukan penelitian lanjutan mengenai konjektur tersebut. Setelah dilakukan penelitian penulis berhasil membuktikan bahwa untuk kasus n bilangan genap solusinya adalah (x,y,n) = (59,6,4) dan (x,y,n) = (221,6,6), sementara untuk kasus n = 3 dengan x genap terbukti hanya terdapat satu pasangan solusi persamaan (x,y) = (248,39). Akan tetapi, untuk kasus n = 3 dengan x bilangan ganjil diatas belum diperoleh hasil yang memuaskan sehingga sangat perlu dilakukan penelitian lanjutan.

On his paper in 2014, Ulas suggests a conjecture about positive integer solutions of equation Ramanujan-Nagell x2 = yn + 2185. In this paper, writer is motivated to conduct advanced research about the conjecture. In this research, writer has successfully proven that in case of n equals even number, the solutions are (x,y,n) = (59,6,4) dan (x,y,n) = (221,6,6), while in case of n = 3 with x is even number, it is proven that there is only one pair solution, that is (x,y) = (248,39). However, for n = 3 case with x is odd number, the satisfied result is not found yet, so the further research has to be done.


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DOI: https://doi.org/10.35799/jm.4.2.2015.8456

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