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On the system of Diophantine equations x+1=3pqa22, x2-x+21=3b22(PDF)

《纺织高校基础科学学报》[ISSN:1006-6977/CN:61-1281/TN]

Issue:
2016年03期
Page:
286-290
Research Field:
Publishing date:

Info

Title:
On the system of Diophantine equations x+1=3pqa22, x2-x+21=3b22
Author(s):
ZHANG Xiaobeng1LI Xiaoxue2
1.School of Science,Xi’an University of Posts and Telecommunications,Xi’an 710121,China; 2.School of Mathematics,Northwest University,Xi’an 710127,China
Keywords:
system of Diophantine equations Pell’s equation positive integer solutions
PACS:
O156.7
DOI:
10.13338/j.issn.1006-8341.2016.03.002
Abstract:
Let p,q be odd primes with 3<p<q.By using the results of quadratic and quartic Diophantine equations with some elementary number theory methods,it is proved that the system of equations x+1=3pqa22,x2-x+21=3b22 has the positive integer solution (x,a,b)=(4 367,4,2 521)if and only if(p,q)=(7,13).

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Last Update: 2016-10-08