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n>1 is an integer.the largest number m,such that n m ​ + 1 divides 1+ n + n 2 ​+ n 3 + ......n 127 ​,is??​

n>1 is an integer.the largest number m,such that nm​ + 1 divides 1+ n + n2 ​+ n3 + ......n127​,is??​

Grade:11

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
5 years ago
The sum of the GP gives
S = \frac{n^{128}-1}{n-1} = \frac{(n^{64}-1)(n^{64}+1)}{n-1}
continuing factorizing further we get
S = \frac{(n-1)(n+1)(n^2+1)(n^4+1)...(n^{64}+1)}{n-1} = (n+1)(n^2+1)(n^4+1)...(n^{64}+1)
Hence the largest m is m=64

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