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The greatest positive integer for which...

The greatest positive integer for which `13 ^(k)+1` is a factor of the sum
`13^(71) + 13 ^(70) + 13 ^(60) +….+ 13+1`

A

35

B

36

C

71

D

72

Text Solution

Verified by Experts

The correct Answer is:
B
`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
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