The greatest +ve integer k, for which 4^...

The greatest +ve integer k, for which `4^k+1` is factor of sum `1+2+2^2+....+2^(99)` is

Verified by Experts

The correct Answer is:

25

`1+2+2^(2)+….2^(99)=2^(100)-1`
`=4^(50)-1=(4^(50)-1)(4^(25)+1)`
`therefore" "k=25`

Similar Questions

Explore conceptually related problems

The greatest positive integer k, for which 81^(k) + 1 is a factor of the sum 9^(350) + 9^(346) …… 9^(4) + 9^(2) + 1

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

Find the greatest value of k for which 49^(k)+1 is a factor of 1+49+49^(2)….(49)^(125)

The largest value of the positive integer k for which n^(k)+1 divides 1+n+n^(2)+ . . . .+n^(127) , is

Determine the value of k for which x+2 is a factor of (x+1)^7+(2x+k)^3dot

Find the value of k, if 2x +1 is a factor of (3k+2)x^3 + (k-1).

Value of k for which x + k is a factor of the polynomial x^(3)+kx^(2)-2x+k+4 is

Find the value of k, if x-1 is a factor of 4x^3+3x^2-4x+k .