The greatest positive integer for which `13 ^(k)+1` is a factor of the sum `13^(71) + 13 ^(70) + 13 ^(69) +….+ 13+1`

Options

A. 35
B. 36
C. 71
D. 72

Answer

B

Explanation

`13^(71) + 13 ^(70) + 13 ^(69) +….+ 13+1`
`= (13 ^(72) -1)/(13-1)= ((13 ^(36) -1) (13 ^(36)+ 1))/(13 -1)`
Greatest value of `K =36`