`5^(2(n-4) -6n + 32` is divisible by 9 for every natural number `n ge 5`.

4^(n+1) + 15n + 14 is divisible by 9 for every natural number n ge 0 .

3^(2(n-1)) + 7 is divisible by 8 for every natural n ge 2 .

7.5^(2n-1) + 2^(3n+1) is divisible by 17 for every natural n ge 1 .

5^n -1 is divisible by 4.

7^(2n) + 2^(3n-3) 3^(n-1) is divisible by 25 for any natural number n gt 1 .

2^n gt n , n is a natural number.

There are 60 tickets in a bag numbered 1 through 60. If a ticket is picked at random, find the probability that the number , on it is divisible by 2 or 5 and is not divisible by any of the numbers 3, 4, 6

If underset(n)(I) is an identity matrix of order n, then k being a natural number, write the matrix underset(n)(I)overset(k) .

The set N of positive natural number set is finite set or infinite set ?

1/(n+1) + 1/(n+2)+…..+ 1/(3n+1) gt 1 for every positive integer n.