Asian Journal of Mathematics & Statistics1994-54182077-2068orgz10.3923/ajms.2009.9.14GhanouchiJamel1200921The Bugeaud-Mignotte theorem concerns the Diophantine equation
,
when X = 10. It includes the fact that any integer greater than 2 and with all
digits equal to 1 in base ten cannot be a pure power. It means that does not
exist Y an integer strictly greater than 1 and q an integer strictly greater
than 1 for which Y^{q} is a number with all digits equal to 1 in base
ten.]]>Bugeaud, Y. and M. Mignotte,1999n-/x-1_{x-1} = y^{q}, II = On the diophantine equation x^{n}-1-_{x-1} = y^{q}, II.]]>