Question

7*. Aratati ca suma a 6 puteri consecutive ale lui 6 se divide cu 133.

Dau coroana!​

Answer 1

a = (6^n)+(6^n+1)+(6^n+2)+(6^n+3)+(6^n+4)+(6^n+5)

= (6^n×1)+(6^n×6)+(6^n×36)+(6^n×216)+(6^n×1296)+(6^n×7776)

= 6^n(1+6+36+216+1296+7776)

= 6^n(9331)

Totusi 9331 nu se divide cu 133, deci nici 6^n(9331) nu se va divide.