Find all natural numbers n such that `1+[ sqrt(2n)]` divides 2n.

The value of the natural numbers n such that 2 ^(n) gt 2n +1 is valid for

If R is a relation on N (set of all natural numbers) defined by n R m iff n divides m, then R is

The relation R on the set N of all natural numbers defined by (x ,\ y) in RhArrx divides y , for all x ,\ y in N is transitive.

If n is a natural number, then sqrt(n) is:

For all natural number of n, 2^(2n).3^(2n)-1-35n is divisible by

Let A = {0, 1} and the set of all natural numbers.Then the mapping f: N rarr A defined by f(2n-1) = 0, f(2n) = 1, AA n in N, is

Show by using the principle of mathematical induction that for all natural number n gt 2, 2^(n) gt 2n+1

If (2^(200)-2^(192).31+2^n) is the perfect square of a natural number , then find the sum of digits of 'n' .

Let P(n) be a statement and let P(n) Rightarrow P(n+1) for all natural number n, then P(n) is true.

By the principle of mathematical induction prove that for all natural numbers 'n' the following statements are true, 2+2^(2)+2^(3)+…..+2^(n)=2(2^(n)-1)