Question 81
Let $M$ be the subset of all numbers from $\{1, 2, \dots, 2015\}$ which are not perfect squares.
a) Prove that $\{\sqrt{n}\} \gt 0.011$ for any $n \in M$.
b) Prove that there exists a number $n \in M$ such that $\{\sqrt{n}\} \lt 0.0115$.
(Here $\{y\}$ stands for the fractional part of $y$.)
a) Prove that $\{\sqrt{n}\} \gt 0.011$ for any $n \in M$.
b) Prove that there exists a number $n \in M$ such that $\{\sqrt{n}\} \lt 0.0115$.
(Here $\{y\}$ stands for the fractional part of $y$.)