Question

Aratati ca numarul $6^{3n+2}+ 6^{3n+1}+1$ este divizibil cu 43. Va rog de clasa a VI-a!

Answer 1

$6^{(3n+2)}+ 6^{(3n+1)}+1= 6^{2}*6^{3n} +6* 6^{3n} +1= 6^{3n} (36+6)+1=$
$216^{n} *42+1= ( M_{43}+1) ^{n} *42+1=42* M_{43}+42* 1^{n} +1=$
$42* M_{43}+43$