Principle of Ma...

For all $$n\in N, \sum n$$ is

If $$49^{n} + 16 n + \lambda$$ is divisible by $$64$$ for all $$n\in N$$, then the least negative integral value of $$\lambda$$ is

Let $$P(m)$$ be the statement $$m^{2}> 100$$, the statement $$P(k + 1)$$ will be true if

Let $$P(n)$$ be a statement such that truth of $$P\left ( n \right )\Rightarrow $$ the truth of $$P\left ( n+1 \right )$$ for all $$n\epsilon N$$, then $$P(n)$$ is true

$$\displaystyle x^{3^{n}}+y^{3^{n}}$$ is divisible by $$x+y$$, if 

For $$n \in N, x^{n + 1} + (x + 1)^{2n - 1}$$ is divisible by

Statement  1 : For each natural number $$n, (n + 1)^7 - n^7 - 1$$ is divisible by 7.
Statement  2 : For each natural $$n$$, $$n^7 - n$$ is divisible by 7.

Let $$P\left ( n \right )=n\left ( n+1 \right )$$ is an even number, then which of the following satisfy $$P(n)$$

For each natural number, the statement $$P\left ( n \right )=2^{3n}-1$$ is divisible by

Let $$P\left ( n \right ):n^{2}+n$$ is an odd integer
$$P\left ( k \right )\Rightarrow P\left ( k+1 \right )$$ is true
Then $$P\left ( n \right )$$ is true for all