Question

Aratati ca 6+6²+6³+.....6 la 21 este divizibil cu 43 Repede va rog

Answer 1

$6+ 6^{2}+6^{3}+...+ 6^{21}=(6+6^{2}+6^{3})+(6^{4}+6^{5}+6^{6})+...+(6^{19}$$+6^{20}+6^{21})=$ Dam factor comun in fiecare paranteza si avem: 
$=6^*(1+6+6^{2})+6^{4}*(1+6+6^{2})+...+6^{19}*(1+6+6^{2})=6*43+$$6^{4}*43+...+6^{19}*43=43*(6+6^{4}+...+6^{19})$ $- Multiplu$ $de$ $43.$