Parametric Solutions of the Diophantine Equation A²+nB⁴=C³

• Autorzy: Jena S. K.

Identyfikatory

DOI

10.4064/ba62-3-2

• Języki publikacji: EN

Abstrakty

EN

The Diophantine equation A²+nB⁴=C³ has infinitely many integral solutions A,B,C for any fixed integer n. The case n=0 is trivial. By using a new polynomial identity we generate these solutions, and then give conditions when the solutions are pairwise co-prime.

Słowa kluczowe

EN

parametric solution; diophantine equation; Diophantine equation A2 + nB4 = C3

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2014
• Tom: Vol. 62, no. 3
• Strony: 211--214
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Jena S. K.

• Department of Electronics & Telecommunication Engineering, KIIT University, Bhubaneswar 751024, Odisha, India

Bibliografia

• [1] F. Beukers, The Diophantine equation Axp + Byq = Czr, Duke Math. J. 91 (1998), 61–88.
• [2] S. K. Jena, Method of infinite ascent applied on mA6 +nB3 = C2, Math. Student 77 (2008), 239–246.
• [3] S. K. Jena, Method of infinite ascent applied on A4 ± nB2 = C3, Math. Student 78 (2009), 233–238.
• [4] S. K. Jena, Method of infinite ascent applied on mA3 +nB3 = C2, Math. Student 79 (2010), 187–192.
• [5] S. K. Jena, Beyond the method of infinite descent, J. Combin. Inform. System Sci. 35 (2010), 501–511.
• [6] S. K. Jena, Method of infinite ascent applied on mA3 + nB3 = 3C2, Math. Student 81 (2012), 151–160.
• [7] S. K. Jena, The method of infinite ascent applied on A4 ± nB3 = C2, Czechoslovak Math. J. 63 (138) (2013), 369–374.
• [8] S. K. Jena, Method of infinite ascent applied on A3 ± nB2 = C3, Notes Number Theory Discrete Math. 19 (2013), no. 2, 10–14.
• [9] S. K. Jena, Method of infinite ascent applied on − (2p A6)+B3 = C2, Comm. Math. 21 (2013), 173–178.