On the Diophantine Equation x(x+1) (x+2) - 2py^n
Abstract：Let p be an odd prime. In this paper, we prove that:① if n〉2 is an integer, then the Dio-phantine equation x(x+l ) (x+2)= 2py^n has only positive integral solution (p,x,y)= (3,1,1) ; ②if n=2,p≠l(mod 8) (p,x,y)= (3,1 integral solution = 17 and tn+2 =6 2pyn has only positive integral solution 2, p≡1 ( mod 8 ) , then it has positive satisfying Sn+2 = 65n+1-Sn, with s1 = 3, s2= 17 and tn+2 =6tn+1 -tn with t1 = 1 ,t2 =6 andpun2 = 16t.+1.2
Keywords：Diophantine equationLucas's problempositive integral solution
Publication Date：2012-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：5( 404-408 )