|Table of Contents|

On the positive integer solution of Diophantine equation x(x+1)(x+2)(x+3)=42y(y+1)(y+2)(y+3)(PDF)

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

Issue:
2019年03期
Page:
293-297
Research Field:
基础科学
Publishing date:

Info

Title:
On the positive integer solution of Diophantine equation x(x+1)(x+2)(x+3)=42y(y+1)(y+2)(y+3)
Author(s):
 LI JianglongLUO MingLIN Lijuan
 School of Mathematics Science, Chongqing Normal University, Chongqing 401331,China
Keywords:
 Diophantine equation recursive sequence congruence positive integer solution
PACS:
O 156.2
DOI:
10.13338/j.issn.1006-8341.2019.03.011
Abstract:
As M,N are both given positive integer,to solve the resolution problem about the Diophantine equation Mx(x+1)(x+2)(x+3)=Ny(y+1)(y+2)(y+3). Based on the basic solution of Pell equation, recursive sequence,congruence theory and other elementary methods,it is proved that when(M,N)=(1,42)the Diophantine equation has only one positive integer solution,that is (x,y)=(7,2).Further improving that N≤50 has positive integer solution when M=1.

References:

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Last Update: 2019-10-07