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n>1 is an integar. the largest m, such that n ^m +1 divides 1+n+n^2+n^3+.......+n^127,is a)127 b)63 c)64 d)32

n>1 is an integar. the largest m, such that n^m +1 divides 1+n+n^2+n^3+.......+n^127,is
a)127 b)63 c)64 d)32

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Please find the answer to your question below
Given series is 1+n+n^2+n^3+.......+n^127
as it is in GP with common ratio n and a=1
We get the sum as=(n128-1)/(n-1)
=(n64+1)(n64-1)/(n-1)
So the largest m in nm+1 which divides the above given expression is 64.

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