`N=2^(n-1)(2^n-1) and (2^n-1)` is a prime number. ` < d_1 < d_2 <.....< d_k=N` are the divisors of `N.` Show that `1/1+1/d_1+1/d_2+.......+1/d_k=2.`

Given that N = 2^(n)(2^(n+1) -1) and 2^(n+1) - 1 is a prime number, which of the following is true, where n is a natural number.

Given that N = 2^(n)(2^(n+1) -1) and 2^(n+1) - 1 is a prime number, which of the following is true, where n is a natural number.

If N=2^(n-1).(2^n-1) where 2^n-1 is a prime, then the sum of the all divisors of N is

If N=2^(n-1)*(2^(n)-1) where 2^(n)-1 is a prime,then the sum of the all divisors of N is

If A = [(1,1),(1,1)] , prove by induction that A^n = [(2^(n-1), 2^(n-1)), (2^(n-1), 2^(n-1))] for all natural numbers n.

P(n) : 2^(2^n) + 1 is a prime number . For n = ………., it is not true .

P(n):2^n - 1 , for n = ……………it is a prime number.

For each n, (2^((2^n)+1))) is a prime n in N

If n^(2)-11n+24=0 is satisfied by n_(1)&n_(2) where n_(2)gtn_(1) then (A) n_(1)^(2)+n_(2) is prime number (B) n_(1)&n_(2)-n_(1) are co-prime (C) n_(1)&n_(2)-n_(1) are twin primes (D) n_(1)+n_(2)+n_(1)n_(2) has 2 prime divisors

If n^(2)-11n+24=0 is satisfied by n_(1)&n_(2) where n_(2)gtn_(1) then (A) n_(1)^(2)+n_(2) is prime number (B) n_(1)&n_(2)-n_(1) are co-prime (C) n_(1)&n_(2)-n_(1) are twin primes (D) n_(1)+n_(2)+n_(1)n_(2) has 2 prime divisors