Question

Oricare ar fi cifrele a,b,c , aratati ca numarul abc +bca+cab+2013 se divide cu 3 .
Multumesc !

Answer 1

100a+10b+c+100b+10c+a+100c+10a+b+2013
⇒111a+111b+111c+2013
⇒111[a+b+c]+2013
⇒3/111⇒111=3·37 respectiv 3/2013⇒2013=3·671;oricare ar fi a,b,c∈N
⇒suma va fi multiplu de 3 oricare ar fi a,b,c∈N;