Open AccessA remark on the Diophantine equation (x^3-1)/(x-1)=(y^n-1)/(y-1)
Author(s) -
Bing He
Publication year - 2009
Publication title -
glasnik matematički
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.332
H-Index - 17
eISSN - 1846-7989
pISSN - 0017-095X
DOI - 10.3336/gm.44.1.01
Subject(s) - diophantine equation , mathematics , diophantine set , thue equation , discrete mathematics , pure mathematics , combinatorics
In this remark, we use some properties of simple continued fractions of quadratic irrational numbers to prove that the equation (x^3 - 1)/(x - 1) = (y^n - 1)/(y - 1), x, y, n in N, x > 1, y > 1, y > 3, n odd, has only the solutions (x,y,n) = (5,2,5) and (90,2,13)