6^2019-6=6(6^2018-1)=6*(6-1)(6^2017+6^2016+....+6³+6²+6+1)=
=6*5*(6^2016 (6+1) +6^2014(6+1)+...+6²(6+1)+(6+1))=
=6*5*7*(6^2016 +6^2014+,,,+6² +6^0) divizibil cu 5*7
C.C.T.D.
EXTRA
am considerat cunoscuta formula a^n-1= (a-1) (a^(n-1) +a^(n-2)+....+a²+a+1)
cum au considerat-o si autorii problemei
