PDF(416 KB)
PDF(416 KB)
PDF(416 KB)
Pell方程组x2-(c2-1)y2=y2-2p1p2p3z2=1的公解
On the Common Solutions of Pell Equations x2-(c2-1)y2=y2-2p1p2p3z2=1
设p1，p2，p3为不同的奇素数，c > 1是整数.给出了Pell方程组x2-（c2-1）y2=y2-2p1p2p3z2=1的所有非负整数解（x，y，z），从而推广了Keskin（2017）和Cipu（2018）等人的结果.
Let p1, p2, p3 be diverse odd primes, and c > 1 be integer. We obtain all nonnegative integer solutions(x, y, z) on the Pell equations x2-(c2-1)y2=y2-2p1p2p3z2=1. It generalizes the previous work of Keskin (2017) and Cipu (2018).
Pell方程 / 基本解 / 公解 / 素数 {{custom_keyword}} /
Pell equation / fundamental solution / common solution / prime {{custom_keyword}} /
[1] Bennett M. A., On the number of solutions of simultaneous Pell equations, J. Reine Angew. Math., 1998, 498:173-199.
[2] Bosma W., Cannon J., Playoust C., The Magma algebra system, I:the user language, J. Symb. Comput., 1997, 24(3-4):235-265.
[3] Cao Z. F., Complete solution of the diophantine equation A2x4-By2=1 and some related problems, J. of Harbin Institute of Technology (New Series), 2001, 8(2):108-110.
[4] Cao Z. F., Diophantine Equation and Its Applications (in Chinese), Shanghai Jiaotong University Press, Shanghai, 2000.
[5] Cipu M., Pairs of Pell equations having at most one common solution in positive integers, An. St. Univ. Ovidius Constant a Ser. Math., 2007, 15(1):55-66.
[6] Cipu M., Explicit formula for the solution of simultaneous Pell equations x2-(a2-1)y2=1, y2-bz2=1, Proceedings of the American Math. Soc., 2018, 146(3):983-992.
[7] Dong X. L., Shiu W. C., Chu C. I., et al., The simultaneous Pell equations y2 -Dz2=1 and x2-2Dz2=1, Acta Arith., 2007, 126(2):115-123.
[8] Guan X. G., On positive integer solutions to the simultaneous Pell equations y2 -Dz2=1 and x2 -2Dz2=1(in Chinese), J. Central China Normal University (Nat. Sci.), 2019, 53(2):171-180.
[9] He B., On the number of solutions of simultaneous Pell equations x2-ay2=1 and y2-bz2=1, Acta Mathematica Sinica, Chinese Series, 2008, 51(4):721-726.
[10] Keskin R., Karaath O., Siar Z., et al., On the determination of solutions of simultaneous Pell equationsx2-(a2-1)y2=y2-pz2=1, Period. Math. Hungar., 2017, 75(2):336-344.
[11] Ljunggren W., Litt om simultane Pellske ligninger, Norsk Mat. Tidsskr., 1941, 2:132-138.
[12] Mignotte M., Pethö A., Sur les carrés dans certaines suites de Lucas, J. Théor. Nombers Bordeaux, 1993, 5(2):333-341.
[13] Sun Q., Yuan P. Z., On the Diophantine equation x4 -Dy2=1(in Chinese), J. Sichuan University (Natural Science Edition), 1997, 34(3):265-268.
[14] Togbe A., Voutier P. M., Walsh P. G., Solving a family of thue equations with an application to the equation x2-Dy4=1, Acta Arith., 2005, 120(1):39-58.
[15] Walsh G., A note on a theorem of Ljunggren and the diophantine equations x2-kxy2 + y4=1 or 4, Arch. Math., 1999, 73(2):119-125.
[16] Yuan P. Z., Simultaneous Pell equations, Acta Arith., 2004, 115:215-221.
[17] Yuan P. Z., On the number of solutions of x2-4m(m +1)y2=y2-bz2=1, Proc. Amer. Math. Soc., 2004, 132:1561-1566.
国家自然科学基金资助项目（11471144）；江苏省自然科学基金资助项目（BK20171318）；云南省教育厅科学研究基金（2019J1182）；泰州学院教博基金项目（TZXY2018JBJJ002）
/
| 〈 |
|
〉 |
