Question

Show that there are infinitely many positive real numbers a which are not integers such that a(a–3{a} is an integer. (Here {a} denotes the fractional part of a. For example {1.5} = 0.5; {–3.4} = 0.6.).

Answer 1

Let a = I + f

For any I, we get possible values of K which makes given expression an integer.