Find the number of positive integers n. such that `sqrtn+sqrt(n+1)< 11.`

Find the number of positive integers n.such that sqrt(n)+sqrt(n+1)<11

Find the number of positive integers n such that 105 is a divisor of n^(2)+n+1

Find the number of positive integers n such that 105 is a divisor of n^2+n+1.

Find the smallest positive integer a such that sqrt(n)-sqrt(n-1)<0.01

If phi(n) denotes the number of positive integers less than n and relatively prime to n and A={n| phi(n)=17}, then find the number of elements in set A.

Show that there is no positive integer, n for which sqrt(n-1) + sqrt(n+1) is rational .