The negation of the statement "For every real number $x ; x^2+5$ is positive" is

The contrapositive of the statement.

"If two lines do not intersect in the same plane, then they are parallel." is

If $$P(n): 2^n< n !$$ Then the smallest positive integer for which $$P(n)$$ is true if

The negation of the statement "For all real numbers $$x$$ and $$y, x+y=y+x^{\prime \prime}$$ is

The negative of the statement "All continuous functions are differentiable."

$P  (n): 2^{2 n}-1$ is divisible by $k$ for all $n \in N^{\prime \prime}$ is true, then the value of ' $k$ ' is